[{"publication_status":"epub_ahead","citation":{"ama":"Davoli E, D’Elia L, Ingmanns J. Stochastic homogenization of micromagnetic energies and emergence of magnetic skyrmions. <i>Journal of Nonlinear Science</i>. 2024;34(2). doi:<a href=\"https://doi.org/10.1007/s00332-023-10005-3\">10.1007/s00332-023-10005-3</a>","mla":"Davoli, Elisa, et al. “Stochastic Homogenization of Micromagnetic Energies and Emergence of Magnetic Skyrmions.” <i>Journal of Nonlinear Science</i>, vol. 34, no. 2, 30, Springer Nature, 2024, doi:<a href=\"https://doi.org/10.1007/s00332-023-10005-3\">10.1007/s00332-023-10005-3</a>.","short":"E. Davoli, L. D’Elia, J. Ingmanns, Journal of Nonlinear Science 34 (2024).","ista":"Davoli E, D’Elia L, Ingmanns J. 2024. Stochastic homogenization of micromagnetic energies and emergence of magnetic skyrmions. Journal of Nonlinear Science. 34(2), 30.","ieee":"E. Davoli, L. D’Elia, and J. Ingmanns, “Stochastic homogenization of micromagnetic energies and emergence of magnetic skyrmions,” <i>Journal of Nonlinear Science</i>, vol. 34, no. 2. Springer Nature, 2024.","apa":"Davoli, E., D’Elia, L., &#38; Ingmanns, J. (2024). Stochastic homogenization of micromagnetic energies and emergence of magnetic skyrmions. <i>Journal of Nonlinear Science</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00332-023-10005-3\">https://doi.org/10.1007/s00332-023-10005-3</a>","chicago":"Davoli, Elisa, Lorenza D’Elia, and Jonas Ingmanns. “Stochastic Homogenization of Micromagnetic Energies and Emergence of Magnetic Skyrmions.” <i>Journal of Nonlinear Science</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s00332-023-10005-3\">https://doi.org/10.1007/s00332-023-10005-3</a>."},"abstract":[{"text":"We perform a stochastic homogenization analysis for composite materials exhibiting a random microstructure. Under the assumptions of stationarity and ergodicity, we characterize the Gamma-limit of a micromagnetic energy functional defined on magnetizations taking value in the unit sphere and including both symmetric and antisymmetric exchange contributions. This Gamma-limit corresponds to a micromagnetic energy functional with homogeneous coefficients. We provide explicit formulas for the effective magnetic properties of the composite material in terms of homogenization correctors. Additionally, the variational analysis of the two exchange energy terms is performed in the more general setting of functionals defined on manifold-valued maps with Sobolev regularity, in the case in which the target manifold is a bounded, orientable smooth surface with tubular neighborhood of uniform thickness. Eventually, we present an explicit characterization of minimizers of the effective exchange in the case of magnetic multilayers, providing quantitative evidence of Dzyaloshinskii’s predictions on the emergence of helical structures in composite ferromagnetic materials with stochastic microstructure.","lang":"eng"}],"author":[{"first_name":"Elisa","last_name":"Davoli","full_name":"Davoli, Elisa"},{"first_name":"Lorenza","last_name":"D’Elia","full_name":"D’Elia, Lorenza"},{"id":"71523d30-15b2-11ec-abd3-f80aa909d6b0","last_name":"Ingmanns","full_name":"Ingmanns, Jonas","first_name":"Jonas"}],"arxiv":1,"date_updated":"2024-02-05T08:54:44Z","volume":34,"oa":1,"article_processing_charge":"No","_id":"14884","publication_identifier":{"eissn":["1432-1467"],"issn":["0938-8974"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","acknowledgement":"All authors acknowledge support of the Austrian Science Fund (FWF) through the SFB project F65. The research of E. Davoli and L. D’Elia has additionally been supported by the FWF through grants V662, Y1292, and P35359, as well as from OeAD through the WTZ grant CZ09/2023.","oa_version":"Preprint","project":[{"grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems"}],"quality_controlled":"1","year":"2024","doi":"10.1007/s00332-023-10005-3","title":"Stochastic homogenization of micromagnetic energies and emergence of magnetic skyrmions","external_id":{"arxiv":["2306.05151"]},"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2306.05151","open_access":"1"}],"article_number":"30","day":"23","type":"journal_article","intvolume":"        34","status":"public","issue":"2","publication":"Journal of Nonlinear Science","month":"01","article_type":"original","date_published":"2024-01-23T00:00:00Z","publisher":"Springer Nature","scopus_import":"1","language":[{"iso":"eng"}],"department":[{"_id":"JuFi"}],"date_created":"2024-01-28T23:01:42Z"},{"scopus_import":"1","title":"A discovery tour in random Riemannian geometry","publisher":"Springer Nature","language":[{"iso":"eng"}],"doi":"10.1007/s11118-023-10118-0","month":"01","year":"2024","article_type":"original","date_published":"2024-01-26T00:00:00Z","date_created":"2024-02-04T23:00:54Z","main_file_link":[{"url":"https://doi.org/10.1007/s11118-023-10118-0","open_access":"1"}],"department":[{"_id":"JaMa"}],"abstract":[{"text":"We study random perturbations of a Riemannian manifold (M, g) by means of so-called\r\nFractional Gaussian Fields, which are defined intrinsically by the given manifold. The fields\r\nh• : ω \u0002→ hω will act on the manifold via the conformal transformation g \u0002→ gω := e2hω g.\r\nOur focus will be on the regular case with Hurst parameter H > 0, the critical case H = 0\r\nbeing the celebrated Liouville geometry in two dimensions. We want to understand how basic\r\ngeometric and functional-analytic quantities like diameter, volume, heat kernel, Brownian\r\nmotion, spectral bound, or spectral gap change under the influence of the noise. And if so, is\r\nit possible to quantify these dependencies in terms of key parameters of the noise? Another\r\ngoal is to define and analyze in detail the Fractional Gaussian Fields on a general Riemannian\r\nmanifold, a fascinating object of independent interest.","lang":"eng"}],"status":"public","author":[{"last_name":"Dello Schiavo","full_name":"Dello Schiavo, Lorenzo","orcid":"0000-0002-9881-6870","first_name":"Lorenzo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E"},{"last_name":"Kopfer","full_name":"Kopfer, Eva","first_name":"Eva"},{"first_name":"Karl Theodor","full_name":"Sturm, Karl Theodor","last_name":"Sturm"}],"citation":{"chicago":"Dello Schiavo, Lorenzo, Eva Kopfer, and Karl Theodor Sturm. “A Discovery Tour in Random Riemannian Geometry.” <i>Potential Analysis</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s11118-023-10118-0\">https://doi.org/10.1007/s11118-023-10118-0</a>.","ieee":"L. Dello Schiavo, E. Kopfer, and K. T. Sturm, “A discovery tour in random Riemannian geometry,” <i>Potential Analysis</i>. Springer Nature, 2024.","apa":"Dello Schiavo, L., Kopfer, E., &#38; Sturm, K. T. (2024). A discovery tour in random Riemannian geometry. <i>Potential Analysis</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s11118-023-10118-0\">https://doi.org/10.1007/s11118-023-10118-0</a>","ista":"Dello Schiavo L, Kopfer E, Sturm KT. 2024. A discovery tour in random Riemannian geometry. Potential Analysis.","short":"L. Dello Schiavo, E. Kopfer, K.T. Sturm, Potential Analysis (2024).","ama":"Dello Schiavo L, Kopfer E, Sturm KT. A discovery tour in random Riemannian geometry. <i>Potential Analysis</i>. 2024. doi:<a href=\"https://doi.org/10.1007/s11118-023-10118-0\">10.1007/s11118-023-10118-0</a>","mla":"Dello Schiavo, Lorenzo, et al. “A Discovery Tour in Random Riemannian Geometry.” <i>Potential Analysis</i>, Springer Nature, 2024, doi:<a href=\"https://doi.org/10.1007/s11118-023-10118-0\">10.1007/s11118-023-10118-0</a>."},"day":"26","publication_status":"epub_ahead","type":"journal_article","publication_identifier":{"issn":["0926-2601"],"eissn":["1572-929X"]},"_id":"14934","project":[{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504"}],"oa_version":"Published Version","quality_controlled":"1","acknowledgement":"The authors would like to thank Matthias Erbar and Ronan Herry for valuable discussions on this project. They are also grateful to Nathanaël Berestycki, and Fabrice Baudoin for respectively pointing out the references [7], and [6, 24], and to Julien Fageot and Thomas Letendre for pointing out a mistake in a previous version of the proof of Proposition 3.10. The authors feel very much indebted to an anonymous reviewer for his/her careful reading and the many valuable suggestions that have significantly contributed to the improvement of the paper. L.D.S. gratefully acknowledges financial support by the Deutsche Forschungsgemeinschaft through CRC 1060 as well as through SPP 2265, and by the Austrian Science Fund (FWF) grant F65 at Institute of Science and Technology Austria. This research was funded in whole or in part by the Austrian Science Fund (FWF) ESPRIT 208. For the purpose of open access, the authors have applied a CC BY public copyright licence to any Author Accepted Manuscript version arising from this submission. E.K. and K.-T.S. gratefully acknowledge funding by the Deutsche Forschungsgemeinschaft through the Hausdorff Center for Mathematics and through CRC 1060 as well as through SPP 2265.\r\nOpen Access funding enabled and organized by Projekt DEAL.","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication":"Potential Analysis","article_processing_charge":"Yes (via OA deal)","date_updated":"2024-02-05T13:04:23Z","oa":1},{"type":"journal_article","day":"05","status":"public","publication":"Neural Computing and Applications","article_type":"original","date_published":"2023-10-05T00:00:00Z","month":"10","language":[{"iso":"eng"}],"scopus_import":"1","publisher":"Springer Nature","department":[{"_id":"JuFi"}],"date_created":"2023-10-22T22:01:16Z","citation":{"ista":"Cornalba F, Disselkamp C, Scassola D, Helf C. 2023. Multi-objective reward generalization: improving performance of Deep Reinforcement Learning for applications in single-asset trading. Neural Computing and Applications.","short":"F. Cornalba, C. Disselkamp, D. Scassola, C. Helf, Neural Computing and Applications (2023).","ama":"Cornalba F, Disselkamp C, Scassola D, Helf C. Multi-objective reward generalization: improving performance of Deep Reinforcement Learning for applications in single-asset trading. <i>Neural Computing and Applications</i>. 2023. doi:<a href=\"https://doi.org/10.1007/s00521-023-09033-7\">10.1007/s00521-023-09033-7</a>","mla":"Cornalba, Federico, et al. “Multi-Objective Reward Generalization: Improving Performance of Deep Reinforcement Learning for Applications in Single-Asset Trading.” <i>Neural Computing and Applications</i>, Springer Nature, 2023, doi:<a href=\"https://doi.org/10.1007/s00521-023-09033-7\">10.1007/s00521-023-09033-7</a>.","chicago":"Cornalba, Federico, Constantin Disselkamp, Davide Scassola, and Christopher Helf. “Multi-Objective Reward Generalization: Improving Performance of Deep Reinforcement Learning for Applications in Single-Asset Trading.” <i>Neural Computing and Applications</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00521-023-09033-7\">https://doi.org/10.1007/s00521-023-09033-7</a>.","apa":"Cornalba, F., Disselkamp, C., Scassola, D., &#38; Helf, C. (2023). Multi-objective reward generalization: improving performance of Deep Reinforcement Learning for applications in single-asset trading. <i>Neural Computing and Applications</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00521-023-09033-7\">https://doi.org/10.1007/s00521-023-09033-7</a>","ieee":"F. Cornalba, C. Disselkamp, D. Scassola, and C. Helf, “Multi-objective reward generalization: improving performance of Deep Reinforcement Learning for applications in single-asset trading,” <i>Neural Computing and Applications</i>. Springer Nature, 2023."},"publication_status":"epub_ahead","author":[{"id":"2CEB641C-A400-11E9-A717-D712E6697425","orcid":"0000-0002-6269-5149","full_name":"Cornalba, Federico","last_name":"Cornalba","first_name":"Federico"},{"first_name":"Constantin","last_name":"Disselkamp","full_name":"Disselkamp, Constantin"},{"last_name":"Scassola","full_name":"Scassola, Davide","first_name":"Davide"},{"last_name":"Helf","full_name":"Helf, Christopher","first_name":"Christopher"}],"abstract":[{"text":"We investigate the potential of Multi-Objective, Deep Reinforcement Learning for stock and cryptocurrency single-asset trading: in particular, we consider a Multi-Objective algorithm which generalizes the reward functions and discount factor (i.e., these components are not specified a priori, but incorporated in the learning process). Firstly, using several important assets (BTCUSD, ETHUSDT, XRPUSDT, AAPL, SPY, NIFTY50), we verify the reward generalization property of the proposed Multi-Objective algorithm, and provide preliminary statistical evidence showing increased predictive stability over the corresponding Single-Objective strategy. Secondly, we show that the Multi-Objective algorithm has a clear edge over the corresponding Single-Objective strategy when the reward mechanism is sparse (i.e., when non-null feedback is infrequent over time). Finally, we discuss the generalization properties with respect to the discount factor. The entirety of our code is provided in open-source format.","lang":"eng"}],"article_processing_charge":"Yes (via OA deal)","date_updated":"2023-10-31T10:58:28Z","oa":1,"arxiv":1,"project":[{"grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"},{"call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411"}],"quality_controlled":"1","oa_version":"Published Version","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","acknowledgement":"Open access funding provided by Università degli Studi di Trieste within the CRUI-CARE Agreement. Funding was provided by Austrian Science Fund (Grant No. F65), Horizon 2020 (Grant No. 754411) and Österreichische Forschungsförderungsgesellschaft.","publication_identifier":{"eissn":["1433-3058"],"issn":["0941-0643"]},"_id":"14451","ec_funded":1,"doi":"10.1007/s00521-023-09033-7","year":"2023","title":"Multi-objective reward generalization: improving performance of Deep Reinforcement Learning for applications in single-asset trading","external_id":{"arxiv":["2203.04579"]},"main_file_link":[{"url":"https://doi.org/10.1007/s00521-023-09033-7","open_access":"1"}]},{"publication_status":"published","citation":{"ama":"Cornalba F, Shardlow T. The regularised inertial Dean’ Kawasaki equation: Discontinuous Galerkin approximation and modelling for low-density regime. <i>ESAIM: Mathematical Modelling and Numerical Analysis</i>. 2023;57(5):3061-3090. doi:<a href=\"https://doi.org/10.1051/m2an/2023077\">10.1051/m2an/2023077</a>","mla":"Cornalba, Federico, and Tony Shardlow. “The Regularised Inertial Dean’ Kawasaki Equation: Discontinuous Galerkin Approximation and Modelling for Low-Density Regime.” <i>ESAIM: Mathematical Modelling and Numerical Analysis</i>, vol. 57, no. 5, EDP Sciences, 2023, pp. 3061–90, doi:<a href=\"https://doi.org/10.1051/m2an/2023077\">10.1051/m2an/2023077</a>.","ista":"Cornalba F, Shardlow T. 2023. The regularised inertial Dean’ Kawasaki equation: Discontinuous Galerkin approximation and modelling for low-density regime. ESAIM: Mathematical Modelling and Numerical Analysis. 57(5), 3061–3090.","short":"F. Cornalba, T. Shardlow, ESAIM: Mathematical Modelling and Numerical Analysis 57 (2023) 3061–3090.","ieee":"F. Cornalba and T. Shardlow, “The regularised inertial Dean’ Kawasaki equation: Discontinuous Galerkin approximation and modelling for low-density regime,” <i>ESAIM: Mathematical Modelling and Numerical Analysis</i>, vol. 57, no. 5. EDP Sciences, pp. 3061–3090, 2023.","apa":"Cornalba, F., &#38; Shardlow, T. (2023). The regularised inertial Dean’ Kawasaki equation: Discontinuous Galerkin approximation and modelling for low-density regime. <i>ESAIM: Mathematical Modelling and Numerical Analysis</i>. EDP Sciences. <a href=\"https://doi.org/10.1051/m2an/2023077\">https://doi.org/10.1051/m2an/2023077</a>","chicago":"Cornalba, Federico, and Tony Shardlow. “The Regularised Inertial Dean’ Kawasaki Equation: Discontinuous Galerkin Approximation and Modelling for Low-Density Regime.” <i>ESAIM: Mathematical Modelling and Numerical Analysis</i>. EDP Sciences, 2023. <a href=\"https://doi.org/10.1051/m2an/2023077\">https://doi.org/10.1051/m2an/2023077</a>."},"abstract":[{"lang":"eng","text":"The Regularised Inertial Dean–Kawasaki model (RIDK) – introduced by the authors and J. Zimmer in earlier works – is a nonlinear stochastic PDE capturing fluctuations around the meanfield limit for large-scale particle systems in both particle density and momentum density. We focus on the following two aspects. Firstly, we set up a Discontinuous Galerkin (DG) discretisation scheme for the RIDK model: we provide suitable definitions of numerical fluxes at the interface of the mesh elements which are consistent with the wave-type nature of the RIDK model and grant stability of the simulations, and we quantify the rate of convergence in mean square to the continuous RIDK model. Secondly, we introduce modifications of the RIDK model in order to preserve positivity of the density (such a feature only holds in a “high-probability sense” for the original RIDK model). By means of numerical simulations, we show that the modifications lead to physically realistic and positive density profiles. In one case, subject to additional regularity constraints, we also prove positivity. Finally, we present an application of our methodology to a system of diffusing and reacting particles. Our Python code is available in open-source format."}],"author":[{"first_name":"Federico","last_name":"Cornalba","full_name":"Cornalba, Federico","orcid":"0000-0002-6269-5149","id":"2CEB641C-A400-11E9-A717-D712E6697425"},{"full_name":"Shardlow, Tony","last_name":"Shardlow","first_name":"Tony"}],"volume":57,"oa":1,"date_updated":"2023-11-20T08:38:47Z","article_processing_charge":"Yes (in subscription journal)","_id":"14554","publication_identifier":{"issn":["2822-7840"],"eissn":["2804-7214"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","acknowledgement":"The authors thank the anonymous referees for their careful reading of the manuscript and their\r\nvaluable suggestions. FC gratefully acknowledges funding from the Austrian Science Fund (FWF) through the project F65, and from the European Union’s Horizon 2020 research and innovation programme under the Marie Sk lodowska-Curie grant agreement No. 754411 (the latter funding source covered the first part of this project).","oa_version":"Published Version","project":[{"name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504"},{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"quality_controlled":"1","doi":"10.1051/m2an/2023077","year":"2023","ec_funded":1,"title":"The regularised inertial Dean' Kawasaki equation: Discontinuous Galerkin approximation and modelling for low-density regime","tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"related_material":{"link":[{"relation":"software","url":"https://github.com/tonyshardlow/RIDK-FD"}]},"ddc":["510"],"day":"01","type":"journal_article","intvolume":"        57","status":"public","issue":"5","publication":"ESAIM: Mathematical Modelling and Numerical Analysis","file_date_updated":"2023-11-20T08:34:57Z","page":"3061-3090","month":"09","article_type":"original","date_published":"2023-09-01T00:00:00Z","publisher":"EDP Sciences","scopus_import":"1","language":[{"iso":"eng"}],"has_accepted_license":"1","department":[{"_id":"JuFi"}],"date_created":"2023-11-19T23:00:55Z","file":[{"file_size":1508534,"file_name":"2023_ESAIM_Cornalba.pdf","checksum":"3aef1475b1882c8dec112df9a5167c39","date_created":"2023-11-20T08:34:57Z","access_level":"open_access","date_updated":"2023-11-20T08:34:57Z","success":1,"relation":"main_file","content_type":"application/pdf","creator":"dernst","file_id":"14560"}]},{"language":[{"iso":"eng"}],"publisher":"Springer Nature","scopus_import":"1","date_published":"2023-03-01T00:00:00Z","article_type":"original","month":"03","date_created":"2021-10-17T22:01:17Z","file":[{"success":1,"relation":"main_file","content_type":"application/pdf","file_id":"14387","creator":"dernst","file_size":806391,"file_name":"2023_PotentialAnalysis_DelloSchiavo.pdf","checksum":"625526482be300ca7281c91c30d41725","date_created":"2023-10-04T09:18:59Z","access_level":"open_access","date_updated":"2023-10-04T09:18:59Z"}],"department":[{"_id":"JaMa"}],"has_accepted_license":"1","status":"public","intvolume":"        58","type":"journal_article","day":"01","page":"573-615","file_date_updated":"2023-10-04T09:18:59Z","publication":"Potential Analysis","title":"Ergodic decomposition of Dirichlet forms via direct integrals and applications","external_id":{"isi":["000704213400001"],"arxiv":["2003.01366"]},"ec_funded":1,"doi":"10.1007/s11118-021-09951-y","year":"2023","ddc":["510"],"isi":1,"tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"author":[{"first_name":"Lorenzo","orcid":"0000-0002-9881-6870","last_name":"Dello Schiavo","full_name":"Dello Schiavo, Lorenzo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E"}],"abstract":[{"lang":"eng","text":"We study direct integrals of quadratic and Dirichlet forms. We show that each quasi-regular Dirichlet space over a probability space admits a unique representation as a direct integral of irreducible Dirichlet spaces, quasi-regular for the same underlying topology. The same holds for each quasi-regular strongly local Dirichlet space over a metrizable Luzin σ-finite Radon measure space, and admitting carré du champ operator. In this case, the representation is only projectively unique."}],"publication_status":"published","citation":{"apa":"Dello Schiavo, L. (2023). Ergodic decomposition of Dirichlet forms via direct integrals and applications. <i>Potential Analysis</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s11118-021-09951-y\">https://doi.org/10.1007/s11118-021-09951-y</a>","ieee":"L. Dello Schiavo, “Ergodic decomposition of Dirichlet forms via direct integrals and applications,” <i>Potential Analysis</i>, vol. 58. Springer Nature, pp. 573–615, 2023.","chicago":"Dello Schiavo, Lorenzo. “Ergodic Decomposition of Dirichlet Forms via Direct Integrals and Applications.” <i>Potential Analysis</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s11118-021-09951-y\">https://doi.org/10.1007/s11118-021-09951-y</a>.","mla":"Dello Schiavo, Lorenzo. “Ergodic Decomposition of Dirichlet Forms via Direct Integrals and Applications.” <i>Potential Analysis</i>, vol. 58, Springer Nature, 2023, pp. 573–615, doi:<a href=\"https://doi.org/10.1007/s11118-021-09951-y\">10.1007/s11118-021-09951-y</a>.","ama":"Dello Schiavo L. Ergodic decomposition of Dirichlet forms via direct integrals and applications. <i>Potential Analysis</i>. 2023;58:573-615. doi:<a href=\"https://doi.org/10.1007/s11118-021-09951-y\">10.1007/s11118-021-09951-y</a>","ista":"Dello Schiavo L. 2023. Ergodic decomposition of Dirichlet forms via direct integrals and applications. Potential Analysis. 58, 573–615.","short":"L. Dello Schiavo, Potential Analysis 58 (2023) 573–615."},"acknowledgement":"The author is grateful to Professors Sergio Albeverio and Andreas Eberle, and to Dr. Kohei Suzuki, for fruitful conversations on the subject of the present work, and for respectively pointing out the references [1, 13], and [3, 20]. Finally, he is especially grateful to an anonymous Reviewer for their very careful reading and their suggestions which improved the readability of the paper.","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"},{"grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems"},{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020","grant_number":"716117"}],"oa_version":"Published Version","quality_controlled":"1","_id":"10145","publication_identifier":{"issn":["0926-2601"],"eissn":["1572-929X"]},"oa":1,"volume":58,"date_updated":"2023-10-04T09:19:12Z","article_processing_charge":"Yes (via OA deal)","arxiv":1},{"ddc":["510"],"article_number":"76","isi":1,"tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"title":"The Dean-Kawasaki equation and the structure of density fluctuations in systems of diffusing particles","external_id":{"isi":["001043086800001"],"arxiv":["2109.06500"]},"ec_funded":1,"doi":"10.1007/s00205-023-01903-7","year":"2023","quality_controlled":"1","oa_version":"Published Version","project":[{"call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411"},{"name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","acknowledgement":"We thank the anonymous referee for his/her careful reading of the manuscript and valuable suggestions. FC gratefully acknowledges funding from the Austrian Science Fund (FWF) through the project F65, and from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411.\r\nOpen access funding provided by Austrian Science Fund (FWF).","publication_identifier":{"eissn":["1432-0673"],"issn":["0003-9527"]},"_id":"10551","article_processing_charge":"Yes (via OA deal)","volume":247,"oa":1,"date_updated":"2024-01-30T12:10:10Z","arxiv":1,"author":[{"id":"2CEB641C-A400-11E9-A717-D712E6697425","first_name":"Federico","last_name":"Cornalba","full_name":"Cornalba, Federico","orcid":"0000-0002-6269-5149"},{"first_name":"Julian L","orcid":"0000-0002-0479-558X","full_name":"Fischer, Julian L","last_name":"Fischer","id":"2C12A0B0-F248-11E8-B48F-1D18A9856A87"}],"abstract":[{"text":"The Dean–Kawasaki equation—a strongly singular SPDE—is a basic equation of fluctuating hydrodynamics; it has been proposed in the physics literature to describe the fluctuations of the density of N independent diffusing particles in the regime of large particle numbers N≫1. The singular nature of the Dean–Kawasaki equation presents a substantial challenge for both its analysis and its rigorous mathematical justification. Besides being non-renormalisable by the theory of regularity structures by Hairer et al., it has recently been shown to not even admit nontrivial martingale solutions. In the present work, we give a rigorous and fully quantitative justification of the Dean–Kawasaki equation by considering the natural regularisation provided by standard numerical discretisations: We show that structure-preserving discretisations of the Dean–Kawasaki equation may approximate the density fluctuations of N non-interacting diffusing particles to arbitrary order in N−1  (in suitable weak metrics). In other words, the Dean–Kawasaki equation may be interpreted as a “recipe” for accurate and efficient numerical simulations of the density fluctuations of independent diffusing particles.","lang":"eng"}],"citation":{"ista":"Cornalba F, Fischer JL. 2023. The Dean-Kawasaki equation and the structure of density fluctuations in systems of diffusing particles. Archive for Rational Mechanics and Analysis. 247(5), 76.","short":"F. Cornalba, J.L. Fischer, Archive for Rational Mechanics and Analysis 247 (2023).","mla":"Cornalba, Federico, and Julian L. Fischer. “The Dean-Kawasaki Equation and the Structure of Density Fluctuations in Systems of Diffusing Particles.” <i>Archive for Rational Mechanics and Analysis</i>, vol. 247, no. 5, 76, Springer Nature, 2023, doi:<a href=\"https://doi.org/10.1007/s00205-023-01903-7\">10.1007/s00205-023-01903-7</a>.","ama":"Cornalba F, Fischer JL. The Dean-Kawasaki equation and the structure of density fluctuations in systems of diffusing particles. <i>Archive for Rational Mechanics and Analysis</i>. 2023;247(5). doi:<a href=\"https://doi.org/10.1007/s00205-023-01903-7\">10.1007/s00205-023-01903-7</a>","chicago":"Cornalba, Federico, and Julian L Fischer. “The Dean-Kawasaki Equation and the Structure of Density Fluctuations in Systems of Diffusing Particles.” <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00205-023-01903-7\">https://doi.org/10.1007/s00205-023-01903-7</a>.","apa":"Cornalba, F., &#38; Fischer, J. L. (2023). The Dean-Kawasaki equation and the structure of density fluctuations in systems of diffusing particles. <i>Archive for Rational Mechanics and Analysis</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00205-023-01903-7\">https://doi.org/10.1007/s00205-023-01903-7</a>","ieee":"F. Cornalba and J. L. Fischer, “The Dean-Kawasaki equation and the structure of density fluctuations in systems of diffusing particles,” <i>Archive for Rational Mechanics and Analysis</i>, vol. 247, no. 5. Springer Nature, 2023."},"publication_status":"published","date_created":"2021-12-16T12:16:03Z","file":[{"file_id":"14904","creator":"dernst","content_type":"application/pdf","relation":"main_file","success":1,"date_updated":"2024-01-30T12:09:34Z","access_level":"open_access","date_created":"2024-01-30T12:09:34Z","checksum":"4529eeff170b6745a461d397ee611b5a","file_name":"2023_ArchiveRationalMech_Cornalba.pdf","file_size":1851185}],"department":[{"_id":"JuFi"}],"has_accepted_license":"1","language":[{"iso":"eng"}],"scopus_import":"1","publisher":"Springer Nature","date_published":"2023-08-04T00:00:00Z","article_type":"original","month":"08","file_date_updated":"2024-01-30T12:09:34Z","publication":"Archive for Rational Mechanics and Analysis","issue":"5","status":"public","intvolume":"       247","type":"journal_article","day":"04"},{"arxiv":1,"article_processing_charge":"Yes (via OA deal)","volume":24,"oa":1,"date_updated":"2023-08-14T11:39:28Z","publication_identifier":{"issn":["1424-0637"]},"_id":"12087","project":[{"grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020"},{"_id":"eb958bca-77a9-11ec-83b8-c565cb50d8d6","name":"Curvature-dimension in noncommutative analysis","grant_number":"M03337"},{"grant_number":"716117","call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425"},{"grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems"}],"oa_version":"Published Version","quality_controlled":"1","acknowledgement":"H.Z. is supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411 and the Lise Meitner fellowship, Austrian Science Fund (FWF) M3337. M.W. acknowledges support from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 716117) and from the Austrian Science Fund (FWF) through grant number F65. Both authors would like to thank Jan Maas for fruitful discussions and helpful comments. Open access funding provided by Austrian Science Fund (FWF).","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Wirth M, Zhang H. 2023. Curvature-dimension conditions for symmetric quantum Markov semigroups. Annales Henri Poincare. 24, 717–750.","short":"M. Wirth, H. Zhang, Annales Henri Poincare 24 (2023) 717–750.","mla":"Wirth, Melchior, and Haonan Zhang. “Curvature-Dimension Conditions for Symmetric Quantum Markov Semigroups.” <i>Annales Henri Poincare</i>, vol. 24, Springer Nature, 2023, pp. 717–50, doi:<a href=\"https://doi.org/10.1007/s00023-022-01220-x\">10.1007/s00023-022-01220-x</a>.","ama":"Wirth M, Zhang H. Curvature-dimension conditions for symmetric quantum Markov semigroups. <i>Annales Henri Poincare</i>. 2023;24:717-750. doi:<a href=\"https://doi.org/10.1007/s00023-022-01220-x\">10.1007/s00023-022-01220-x</a>","chicago":"Wirth, Melchior, and Haonan Zhang. “Curvature-Dimension Conditions for Symmetric Quantum Markov Semigroups.” <i>Annales Henri Poincare</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00023-022-01220-x\">https://doi.org/10.1007/s00023-022-01220-x</a>.","ieee":"M. Wirth and H. Zhang, “Curvature-dimension conditions for symmetric quantum Markov semigroups,” <i>Annales Henri Poincare</i>, vol. 24. Springer Nature, pp. 717–750, 2023.","apa":"Wirth, M., &#38; Zhang, H. (2023). Curvature-dimension conditions for symmetric quantum Markov semigroups. <i>Annales Henri Poincare</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00023-022-01220-x\">https://doi.org/10.1007/s00023-022-01220-x</a>"},"publication_status":"published","abstract":[{"lang":"eng","text":"Following up on the recent work on lower Ricci curvature bounds for quantum systems, we introduce two noncommutative versions of curvature-dimension bounds for symmetric quantum Markov semigroups over matrix algebras. Under suitable such curvature-dimension conditions, we prove a family of dimension-dependent functional inequalities, a version of the Bonnet–Myers theorem and concavity of entropy power in the noncommutative setting. We also provide examples satisfying certain curvature-dimension conditions, including Schur multipliers over matrix algebras, Herz–Schur multipliers over group algebras and generalized depolarizing semigroups."}],"author":[{"orcid":"0000-0002-0519-4241","last_name":"Wirth","full_name":"Wirth, Melchior","first_name":"Melchior","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E"},{"id":"D8F41E38-9E66-11E9-A9E2-65C2E5697425","first_name":"Haonan","full_name":"Zhang, Haonan","last_name":"Zhang"}],"tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"isi":1,"ddc":["510"],"doi":"10.1007/s00023-022-01220-x","year":"2023","ec_funded":1,"external_id":{"isi":["000837499800002"],"arxiv":["2105.08303"]},"title":"Curvature-dimension conditions for symmetric quantum Markov semigroups","publication":"Annales Henri Poincare","file_date_updated":"2023-08-14T11:38:28Z","page":"717-750","day":"01","type":"journal_article","intvolume":"        24","status":"public","has_accepted_license":"1","department":[{"_id":"JaMa"}],"file":[{"date_created":"2023-08-14T11:38:28Z","checksum":"8c7b185eba5ccd92ef55c120f654222c","file_name":"2023_AnnalesHenriPoincare_Wirth.pdf","file_size":554871,"date_updated":"2023-08-14T11:38:28Z","access_level":"open_access","success":1,"creator":"dernst","file_id":"14051","content_type":"application/pdf","relation":"main_file"}],"date_created":"2022-09-11T22:01:57Z","month":"03","article_type":"original","date_published":"2023-03-01T00:00:00Z","scopus_import":"1","publisher":"Springer Nature","language":[{"iso":"eng"}]},{"doi":"10.1007/s00028-022-00859-7","year":"2023","ec_funded":1,"title":"Ergodic decompositions of Dirichlet forms under order isomorphisms","external_id":{"isi":["000906214600004"]},"tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_number":"9","isi":1,"ddc":["510"],"citation":{"mla":"Dello Schiavo, Lorenzo, and Melchior Wirth. “Ergodic Decompositions of Dirichlet Forms under Order Isomorphisms.” <i>Journal of Evolution Equations</i>, vol. 23, no. 1, 9, Springer Nature, 2023, doi:<a href=\"https://doi.org/10.1007/s00028-022-00859-7\">10.1007/s00028-022-00859-7</a>.","ama":"Dello Schiavo L, Wirth M. Ergodic decompositions of Dirichlet forms under order isomorphisms. <i>Journal of Evolution Equations</i>. 2023;23(1). doi:<a href=\"https://doi.org/10.1007/s00028-022-00859-7\">10.1007/s00028-022-00859-7</a>","short":"L. Dello Schiavo, M. Wirth, Journal of Evolution Equations 23 (2023).","ista":"Dello Schiavo L, Wirth M. 2023. Ergodic decompositions of Dirichlet forms under order isomorphisms. Journal of Evolution Equations. 23(1), 9.","apa":"Dello Schiavo, L., &#38; Wirth, M. (2023). Ergodic decompositions of Dirichlet forms under order isomorphisms. <i>Journal of Evolution Equations</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00028-022-00859-7\">https://doi.org/10.1007/s00028-022-00859-7</a>","ieee":"L. Dello Schiavo and M. Wirth, “Ergodic decompositions of Dirichlet forms under order isomorphisms,” <i>Journal of Evolution Equations</i>, vol. 23, no. 1. Springer Nature, 2023.","chicago":"Dello Schiavo, Lorenzo, and Melchior Wirth. “Ergodic Decompositions of Dirichlet Forms under Order Isomorphisms.” <i>Journal of Evolution Equations</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00028-022-00859-7\">https://doi.org/10.1007/s00028-022-00859-7</a>."},"publication_status":"published","abstract":[{"lang":"eng","text":"We study ergodic decompositions of Dirichlet spaces under intertwining via unitary order isomorphisms. We show that the ergodic decomposition of a quasi-regular Dirichlet space is unique up to a unique isomorphism of the indexing space. Furthermore, every unitary order isomorphism intertwining two quasi-regular Dirichlet spaces is decomposable over their ergodic decompositions up to conjugation via an isomorphism of the corresponding indexing spaces."}],"author":[{"id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","orcid":"0000-0002-9881-6870","last_name":"Dello Schiavo","full_name":"Dello Schiavo, Lorenzo","first_name":"Lorenzo"},{"orcid":"0000-0002-0519-4241","full_name":"Wirth, Melchior","last_name":"Wirth","first_name":"Melchior","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E"}],"article_processing_charge":"Yes (via OA deal)","oa":1,"date_updated":"2023-06-28T11:54:35Z","volume":23,"publication_identifier":{"issn":["1424-3199"],"eissn":["1424-3202"]},"_id":"12104","quality_controlled":"1","project":[{"name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504"},{"grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425","name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020"},{"grant_number":"E208","_id":"34dbf174-11ca-11ed-8bc3-afe9d43d4b9c","name":"Configuration Spaces over Non-Smooth Spaces"},{"_id":"34c6ea2d-11ca-11ed-8bc3-c04f3c502833","name":"Gradient flow techniques for quantum Markov semigroups","grant_number":"ESP156_N"}],"oa_version":"Published Version","acknowledgement":"Research supported by the Austrian Science Fund (FWF) grant F65 at the Institute of Science and Technology Austria and by the European Research Council (ERC) (Grant agreement No. 716117 awarded to Prof. Dr. Jan Maas). L.D.S. gratefully acknowledges funding of his current position by the Austrian Science Fund (FWF) through the ESPRIT Programme (Grant No. 208). M.W. gratefully acknowledges funding of his current position by the Austrian Science Fund (FWF) through the ESPRIT Programme (Grant No. 156).","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","month":"01","article_type":"original","date_published":"2023-01-01T00:00:00Z","scopus_import":"1","publisher":"Springer Nature","language":[{"iso":"eng"}],"has_accepted_license":"1","department":[{"_id":"JaMa"}],"file":[{"creator":"dernst","file_id":"12325","relation":"main_file","content_type":"application/pdf","success":1,"access_level":"open_access","date_updated":"2023-01-20T10:45:06Z","checksum":"1f34f3e2cb521033de6154f274ea3a4e","date_created":"2023-01-20T10:45:06Z","file_size":422612,"file_name":"2023_JourEvolutionEquations_DelloSchiavo.pdf"}],"date_created":"2023-01-08T23:00:53Z","day":"01","type":"journal_article","intvolume":"        23","status":"public","publication":"Journal of Evolution Equations","issue":"1","file_date_updated":"2023-01-20T10:45:06Z"},{"file_date_updated":"2023-10-04T11:34:10Z","publication":"Calculus of Variations and Partial Differential Equations","issue":"5","status":"public","intvolume":"        62","type":"journal_article","day":"28","date_created":"2023-05-14T22:01:00Z","file":[{"success":1,"content_type":"application/pdf","relation":"main_file","creator":"dernst","file_id":"14393","file_name":"2023_CalculusEquations_Gladbach.pdf","file_size":1240995,"date_created":"2023-10-04T11:34:10Z","checksum":"359bee38d94b7e0aa73925063cb8884d","date_updated":"2023-10-04T11:34:10Z","access_level":"open_access"}],"department":[{"_id":"JaMa"}],"has_accepted_license":"1","language":[{"iso":"eng"}],"scopus_import":"1","publisher":"Springer Nature","article_type":"original","date_published":"2023-04-28T00:00:00Z","month":"04","quality_controlled":"1","oa_version":"Published Version","project":[{"grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems"},{"call_identifier":"FWF","_id":"260788DE-B435-11E9-9278-68D0E5697425","name":"Dissipation and Dispersion in Nonlinear Partial Differential Equations"}],"acknowledgement":"J.M. gratefully acknowledges support by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 716117). J.M and L.P. also acknowledge support from the Austrian Science Fund (FWF), grants No F65 and W1245. E.K. gratefully acknowledges support by the German Research Foundation through the Hausdorff Center for Mathematics and the Collaborative Research Center 1060. P.G. is partially funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—350398276. We thank the anonymous reviewer for the careful reading and for useful suggestions. Open access funding provided by Austrian Science Fund (FWF).","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"issn":["0944-2669"],"eissn":["1432-0835"]},"_id":"12959","article_processing_charge":"Yes (via OA deal)","oa":1,"date_updated":"2023-10-04T11:34:49Z","volume":62,"arxiv":1,"author":[{"first_name":"Peter","full_name":"Gladbach, Peter","last_name":"Gladbach"},{"first_name":"Eva","last_name":"Kopfer","full_name":"Kopfer, Eva"},{"orcid":"0000-0002-0845-1338","full_name":"Maas, Jan","last_name":"Maas","first_name":"Jan","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Lorenzo","last_name":"Portinale","full_name":"Portinale, Lorenzo","id":"30AD2CBC-F248-11E8-B48F-1D18A9856A87"}],"abstract":[{"lang":"eng","text":"This paper deals with the large-scale behaviour of dynamical optimal transport on Zd\r\n-periodic graphs with general lower semicontinuous and convex energy densities. Our main contribution is a homogenisation result that describes the effective behaviour of the discrete problems in terms of a continuous optimal transport problem. The effective energy density can be explicitly expressed in terms of a cell formula, which is a finite-dimensional convex programming problem that depends non-trivially on the local geometry of the discrete graph and the discrete energy density. Our homogenisation result is derived from a Γ\r\n-convergence result for action functionals on curves of measures, which we prove under very mild growth conditions on the energy density. We investigate the cell formula in several cases of interest, including finite-volume discretisations of the Wasserstein distance, where non-trivial limiting behaviour occurs."}],"citation":{"ista":"Gladbach P, Kopfer E, Maas J, Portinale L. 2023. Homogenisation of dynamical optimal transport on periodic graphs. Calculus of Variations and Partial Differential Equations. 62(5), 143.","short":"P. Gladbach, E. Kopfer, J. Maas, L. Portinale, Calculus of Variations and Partial Differential Equations 62 (2023).","mla":"Gladbach, Peter, et al. “Homogenisation of Dynamical Optimal Transport on Periodic Graphs.” <i>Calculus of Variations and Partial Differential Equations</i>, vol. 62, no. 5, 143, Springer Nature, 2023, doi:<a href=\"https://doi.org/10.1007/s00526-023-02472-z\">10.1007/s00526-023-02472-z</a>.","ama":"Gladbach P, Kopfer E, Maas J, Portinale L. Homogenisation of dynamical optimal transport on periodic graphs. <i>Calculus of Variations and Partial Differential Equations</i>. 2023;62(5). doi:<a href=\"https://doi.org/10.1007/s00526-023-02472-z\">10.1007/s00526-023-02472-z</a>","chicago":"Gladbach, Peter, Eva Kopfer, Jan Maas, and Lorenzo Portinale. “Homogenisation of Dynamical Optimal Transport on Periodic Graphs.” <i>Calculus of Variations and Partial Differential Equations</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00526-023-02472-z\">https://doi.org/10.1007/s00526-023-02472-z</a>.","ieee":"P. Gladbach, E. Kopfer, J. Maas, and L. Portinale, “Homogenisation of dynamical optimal transport on periodic graphs,” <i>Calculus of Variations and Partial Differential Equations</i>, vol. 62, no. 5. Springer Nature, 2023.","apa":"Gladbach, P., Kopfer, E., Maas, J., &#38; Portinale, L. (2023). Homogenisation of dynamical optimal transport on periodic graphs. <i>Calculus of Variations and Partial Differential Equations</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00526-023-02472-z\">https://doi.org/10.1007/s00526-023-02472-z</a>"},"publication_status":"published","ddc":["510"],"isi":1,"article_number":"143","tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"title":"Homogenisation of dynamical optimal transport on periodic graphs","external_id":{"isi":["000980588900001"],"arxiv":["2110.15321"]},"ec_funded":1,"year":"2023","doi":"10.1007/s00526-023-02472-z"},{"ec_funded":1,"year":"2022","doi":"10.1007/s10955-022-02911-9","external_id":{"isi":["000780305000001"]},"title":"A dual formula for the noncommutative transport distance","isi":1,"article_number":"19","tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"ddc":["510","530"],"citation":{"ieee":"M. Wirth, “A dual formula for the noncommutative transport distance,” <i>Journal of Statistical Physics</i>, vol. 187, no. 2. Springer Nature, 2022.","apa":"Wirth, M. (2022). A dual formula for the noncommutative transport distance. <i>Journal of Statistical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s10955-022-02911-9\">https://doi.org/10.1007/s10955-022-02911-9</a>","chicago":"Wirth, Melchior. “A Dual Formula for the Noncommutative Transport Distance.” <i>Journal of Statistical Physics</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s10955-022-02911-9\">https://doi.org/10.1007/s10955-022-02911-9</a>.","mla":"Wirth, Melchior. “A Dual Formula for the Noncommutative Transport Distance.” <i>Journal of Statistical Physics</i>, vol. 187, no. 2, 19, Springer Nature, 2022, doi:<a href=\"https://doi.org/10.1007/s10955-022-02911-9\">10.1007/s10955-022-02911-9</a>.","ama":"Wirth M. A dual formula for the noncommutative transport distance. <i>Journal of Statistical Physics</i>. 2022;187(2). doi:<a href=\"https://doi.org/10.1007/s10955-022-02911-9\">10.1007/s10955-022-02911-9</a>","short":"M. Wirth, Journal of Statistical Physics 187 (2022).","ista":"Wirth M. 2022. A dual formula for the noncommutative transport distance. Journal of Statistical Physics. 187(2), 19."},"publication_status":"published","author":[{"first_name":"Melchior","orcid":"0000-0002-0519-4241","last_name":"Wirth","full_name":"Wirth, Melchior","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E"}],"abstract":[{"lang":"eng","text":"In this article we study the noncommutative transport distance introduced by Carlen and Maas and its entropic regularization defined by Becker and Li. We prove a duality formula that can be understood as a quantum version of the dual Benamou–Brenier formulation of the Wasserstein distance in terms of subsolutions of a Hamilton–Jacobi–Bellmann equation."}],"article_processing_charge":"Yes (via OA deal)","volume":187,"date_updated":"2023-08-03T06:37:49Z","oa":1,"project":[{"name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504"},{"grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425","name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020"}],"quality_controlled":"1","oa_version":"Published Version","acknowledgement":"The author wants to thank Jan Maas for helpful comments. He also acknowledges financial support from the Austrian Science Fund (FWF) through Grant Number F65 and from the European Research Council (ERC) under the European Union’s Horizon 2020 Research and Innovation Programme (Grant Agreement No. 716117).\r\nOpen access funding provided by Institute of Science and Technology (IST Austria).","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication_identifier":{"eissn":["15729613"],"issn":["00224715"]},"_id":"11330","date_published":"2022-04-08T00:00:00Z","article_type":"original","month":"04","language":[{"iso":"eng"}],"scopus_import":"1","publisher":"Springer Nature","department":[{"_id":"JaMa"}],"has_accepted_license":"1","file":[{"success":1,"content_type":"application/pdf","relation":"main_file","creator":"dernst","file_id":"11338","file_name":"2022_JourStatisticalPhysics_Wirth.pdf","file_size":362119,"date_created":"2022-04-29T11:24:23Z","checksum":"f3e0b00884b7dde31347a3756788b473","date_updated":"2022-04-29T11:24:23Z","access_level":"open_access"}],"date_created":"2022-04-24T22:01:43Z","type":"journal_article","day":"08","status":"public","intvolume":"       187","file_date_updated":"2022-04-29T11:24:23Z","publication":"Journal of Statistical Physics","issue":"2"},{"title":"The Dirichlet–Ferguson diffusion on the space of probability measures over a closed Riemannian manifold","external_id":{"isi":["000773518500005"],"arxiv":["1811.11598"]},"ec_funded":1,"year":"2022","doi":"10.1214/21-AOP1541","isi":1,"main_file_link":[{"open_access":"1","url":" https://doi.org/10.48550/arXiv.1811.11598"}],"author":[{"id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","full_name":"Dello Schiavo, Lorenzo","last_name":"Dello Schiavo","orcid":"0000-0002-9881-6870","first_name":"Lorenzo"}],"abstract":[{"lang":"eng","text":"We construct a recurrent diffusion process with values in the space of probability measures over an arbitrary closed Riemannian manifold of dimension d≥2. The process is associated with the Dirichlet form defined by integration of the Wasserstein gradient w.r.t. the Dirichlet–Ferguson measure, and is the counterpart on multidimensional base spaces to the modified massive Arratia flow over the unit interval described in V. Konarovskyi and M.-K. von Renesse (Comm. Pure Appl. Math. 72 (2019) 764–800). Together with two different constructions of the process, we discuss its ergodicity, invariant sets, finite-dimensional approximations, and Varadhan short-time asymptotics."}],"publication_status":"published","citation":{"short":"L. Dello Schiavo, Annals of Probability 50 (2022) 591–648.","ista":"Dello Schiavo L. 2022. The Dirichlet–Ferguson diffusion on the space of probability measures over a closed Riemannian manifold. Annals of Probability. 50(2), 591–648.","ama":"Dello Schiavo L. The Dirichlet–Ferguson diffusion on the space of probability measures over a closed Riemannian manifold. <i>Annals of Probability</i>. 2022;50(2):591-648. doi:<a href=\"https://doi.org/10.1214/21-AOP1541\">10.1214/21-AOP1541</a>","mla":"Dello Schiavo, Lorenzo. “The Dirichlet–Ferguson Diffusion on the Space of Probability Measures over a Closed Riemannian Manifold.” <i>Annals of Probability</i>, vol. 50, no. 2, Institute of Mathematical Statistics, 2022, pp. 591–648, doi:<a href=\"https://doi.org/10.1214/21-AOP1541\">10.1214/21-AOP1541</a>.","chicago":"Dello Schiavo, Lorenzo. “The Dirichlet–Ferguson Diffusion on the Space of Probability Measures over a Closed Riemannian Manifold.” <i>Annals of Probability</i>. Institute of Mathematical Statistics, 2022. <a href=\"https://doi.org/10.1214/21-AOP1541\">https://doi.org/10.1214/21-AOP1541</a>.","ieee":"L. Dello Schiavo, “The Dirichlet–Ferguson diffusion on the space of probability measures over a closed Riemannian manifold,” <i>Annals of Probability</i>, vol. 50, no. 2. Institute of Mathematical Statistics, pp. 591–648, 2022.","apa":"Dello Schiavo, L. (2022). The Dirichlet–Ferguson diffusion on the space of probability measures over a closed Riemannian manifold. <i>Annals of Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/21-AOP1541\">https://doi.org/10.1214/21-AOP1541</a>"},"acknowledgement":"Research supported by the Sonderforschungsbereich 1060 and the Hausdorff Center for Mathematics. The author gratefully acknowledges funding of his current position at IST Austria by the Austrian Science Fund (FWF) grant F65 and by the European Research Council (ERC, Grant agreement No. 716117, awarded to Prof. Dr. Jan Maas).","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Preprint","project":[{"grant_number":"716117","call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425","name":"Optimal Transport and Stochastic Dynamics"},{"name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504"}],"quality_controlled":"1","_id":"11354","publication_identifier":{"issn":["0091-1798"],"eissn":["2168-894X"]},"volume":50,"oa":1,"date_updated":"2023-10-17T12:50:24Z","article_processing_charge":"No","arxiv":1,"language":[{"iso":"eng"}],"publisher":"Institute of Mathematical Statistics","scopus_import":"1","date_published":"2022-03-01T00:00:00Z","article_type":"original","month":"03","date_created":"2022-05-08T22:01:44Z","department":[{"_id":"JaMa"}],"status":"public","intvolume":"        50","type":"journal_article","day":"01","page":"591-648","issue":"2","publication":"Annals of Probability"},{"isi":1,"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2105.05677"}],"ec_funded":1,"doi":"10.3934/nhm.2022023","year":"2022","external_id":{"arxiv":["2105.05677"],"isi":["000812422100001"]},"title":"Gradient flow formulation of diffusion equations in the Wasserstein space over a metric graph","date_updated":"2023-08-03T12:25:49Z","volume":17,"oa":1,"article_processing_charge":"No","arxiv":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","acknowledgement":"ME acknowledges funding by the Deutsche Forschungsgemeinschaft (DFG), Grant SFB 1283/2 2021 – 317210226. DF and JM were supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 716117). JM also acknowledges support by the Austrian Science Fund (FWF), Project SFB F65. The work of DM was partially supported by the Deutsche Forschungsgemeinschaft\r\n(DFG), Grant 397230547. This article is based upon work from COST Action\r\n18232 MAT-DYN-NET, supported by COST (European Cooperation in Science\r\nand Technology), www.cost.eu. We wish to thank Martin Burger and Jan-Frederik\r\nPietschmann for useful discussions. We are grateful to the anonymous referees for\r\ntheir careful reading and useful suggestions.","project":[{"grant_number":"716117","call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425","name":"Optimal Transport and Stochastic Dynamics"},{"grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"}],"quality_controlled":"1","oa_version":"Preprint","_id":"11700","publication_identifier":{"eissn":["1556-181X"],"issn":["1556-1801"]},"publication_status":"published","citation":{"ama":"Erbar M, Forkert DL, Maas J, Mugnolo D. Gradient flow formulation of diffusion equations in the Wasserstein space over a metric graph. <i>Networks and Heterogeneous Media</i>. 2022;17(5):687-717. doi:<a href=\"https://doi.org/10.3934/nhm.2022023\">10.3934/nhm.2022023</a>","mla":"Erbar, Matthias, et al. “Gradient Flow Formulation of Diffusion Equations in the Wasserstein Space over a Metric Graph.” <i>Networks and Heterogeneous Media</i>, vol. 17, no. 5, American Institute of Mathematical Sciences, 2022, pp. 687–717, doi:<a href=\"https://doi.org/10.3934/nhm.2022023\">10.3934/nhm.2022023</a>.","short":"M. Erbar, D.L. Forkert, J. Maas, D. Mugnolo, Networks and Heterogeneous Media 17 (2022) 687–717.","ista":"Erbar M, Forkert DL, Maas J, Mugnolo D. 2022. Gradient flow formulation of diffusion equations in the Wasserstein space over a metric graph. Networks and Heterogeneous Media. 17(5), 687–717.","ieee":"M. Erbar, D. L. Forkert, J. Maas, and D. Mugnolo, “Gradient flow formulation of diffusion equations in the Wasserstein space over a metric graph,” <i>Networks and Heterogeneous Media</i>, vol. 17, no. 5. American Institute of Mathematical Sciences, pp. 687–717, 2022.","apa":"Erbar, M., Forkert, D. L., Maas, J., &#38; Mugnolo, D. (2022). Gradient flow formulation of diffusion equations in the Wasserstein space over a metric graph. <i>Networks and Heterogeneous Media</i>. American Institute of Mathematical Sciences. <a href=\"https://doi.org/10.3934/nhm.2022023\">https://doi.org/10.3934/nhm.2022023</a>","chicago":"Erbar, Matthias, Dominik L Forkert, Jan Maas, and Delio Mugnolo. “Gradient Flow Formulation of Diffusion Equations in the Wasserstein Space over a Metric Graph.” <i>Networks and Heterogeneous Media</i>. American Institute of Mathematical Sciences, 2022. <a href=\"https://doi.org/10.3934/nhm.2022023\">https://doi.org/10.3934/nhm.2022023</a>."},"author":[{"first_name":"Matthias","last_name":"Erbar","full_name":"Erbar, Matthias"},{"first_name":"Dominik L","full_name":"Forkert, Dominik L","last_name":"Forkert","id":"35C79D68-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0002-0845-1338","last_name":"Maas","full_name":"Maas, Jan","first_name":"Jan","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Delio","full_name":"Mugnolo, Delio","last_name":"Mugnolo"}],"abstract":[{"text":"This paper contains two contributions in the study of optimal transport on metric graphs. Firstly, we prove a Benamou–Brenier formula for the Wasserstein distance, which establishes the equivalence of static and dynamical optimal transport. Secondly, in the spirit of Jordan–Kinderlehrer–Otto, we show that McKean–Vlasov equations can be formulated as gradient flow of the free energy in the Wasserstein space of probability measures. The proofs of these results are based on careful regularisation arguments to circumvent some of the difficulties arising in metric graphs, namely, branching of geodesics and the failure of semi-convexity of entropy functionals in the Wasserstein space.","lang":"eng"}],"department":[{"_id":"JaMa"}],"date_created":"2022-07-31T22:01:46Z","article_type":"original","date_published":"2022-10-01T00:00:00Z","month":"10","language":[{"iso":"eng"}],"publisher":"American Institute of Mathematical Sciences","scopus_import":"1","page":"687-717","issue":"5","publication":"Networks and Heterogeneous Media","type":"journal_article","day":"01","status":"public","intvolume":"        17"},{"intvolume":"        54","status":"public","day":"18","type":"journal_article","publication":"SIAM Journal on Mathematical Analysis","issue":"4","page":"4297-4333","scopus_import":"1","publisher":"Society for Industrial and Applied Mathematics","language":[{"iso":"eng"}],"month":"07","article_type":"original","date_published":"2022-07-18T00:00:00Z","date_created":"2022-08-07T22:01:59Z","department":[{"_id":"JaMa"}],"abstract":[{"text":"We consider finite-volume approximations of Fokker--Planck equations on bounded convex domains in $\\mathbb{R}^d$ and study the corresponding gradient flow structures. We reprove the convergence of the discrete to continuous Fokker--Planck equation via the method of evolutionary $\\Gamma$-convergence, i.e., we pass to the limit at the level of the gradient flow structures, generalizing the one-dimensional result obtained by Disser and Liero. The proof is of variational nature and relies on a Mosco convergence result for functionals in the discrete-to-continuum limit that is of independent interest. Our results apply to arbitrary regular meshes, even though the associated discrete transport distances may fail to converge to the Wasserstein distance in this generality.","lang":"eng"}],"author":[{"id":"35C79D68-F248-11E8-B48F-1D18A9856A87","full_name":"Forkert, Dominik L","last_name":"Forkert","first_name":"Dominik L"},{"full_name":"Maas, Jan","last_name":"Maas","orcid":"0000-0002-0845-1338","first_name":"Jan","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87"},{"id":"30AD2CBC-F248-11E8-B48F-1D18A9856A87","first_name":"Lorenzo","full_name":"Portinale, Lorenzo","last_name":"Portinale"}],"keyword":["Fokker--Planck equation","gradient flow","evolutionary $\\Gamma$-convergence"],"citation":{"short":"D.L. Forkert, J. Maas, L. Portinale, SIAM Journal on Mathematical Analysis 54 (2022) 4297–4333.","ista":"Forkert DL, Maas J, Portinale L. 2022. Evolutionary $\\Gamma$-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions. SIAM Journal on Mathematical Analysis. 54(4), 4297–4333.","ama":"Forkert DL, Maas J, Portinale L. Evolutionary $\\Gamma$-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions. <i>SIAM Journal on Mathematical Analysis</i>. 2022;54(4):4297-4333. doi:<a href=\"https://doi.org/10.1137/21M1410968\">10.1137/21M1410968</a>","mla":"Forkert, Dominik L., et al. “Evolutionary $\\Gamma$-Convergence of Entropic Gradient Flow Structures for Fokker-Planck Equations in Multiple Dimensions.” <i>SIAM Journal on Mathematical Analysis</i>, vol. 54, no. 4, Society for Industrial and Applied Mathematics, 2022, pp. 4297–333, doi:<a href=\"https://doi.org/10.1137/21M1410968\">10.1137/21M1410968</a>.","chicago":"Forkert, Dominik L, Jan Maas, and Lorenzo Portinale. “Evolutionary $\\Gamma$-Convergence of Entropic Gradient Flow Structures for Fokker-Planck Equations in Multiple Dimensions.” <i>SIAM Journal on Mathematical Analysis</i>. Society for Industrial and Applied Mathematics, 2022. <a href=\"https://doi.org/10.1137/21M1410968\">https://doi.org/10.1137/21M1410968</a>.","ieee":"D. L. Forkert, J. Maas, and L. Portinale, “Evolutionary $\\Gamma$-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions,” <i>SIAM Journal on Mathematical Analysis</i>, vol. 54, no. 4. Society for Industrial and Applied Mathematics, pp. 4297–4333, 2022.","apa":"Forkert, D. L., Maas, J., &#38; Portinale, L. (2022). Evolutionary $\\Gamma$-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions. <i>SIAM Journal on Mathematical Analysis</i>. Society for Industrial and Applied Mathematics. <a href=\"https://doi.org/10.1137/21M1410968\">https://doi.org/10.1137/21M1410968</a>"},"publication_status":"published","publication_identifier":{"eissn":["1095-7154"],"issn":["0036-1410"]},"_id":"11739","project":[{"call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117"},{"grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems"},{"call_identifier":"FWF","_id":"260788DE-B435-11E9-9278-68D0E5697425","name":"Dissipation and Dispersion in Nonlinear Partial Differential Equations"}],"oa_version":"Preprint","quality_controlled":"1","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","acknowledgement":"This work was supported by the European Research Council (ERC) under the European Union's Horizon 2020 Research and Innovation Programme grant 716117 and by the AustrianScience Fund (FWF) through grants F65 and W1245.","arxiv":1,"article_processing_charge":"No","oa":1,"volume":54,"date_updated":"2023-08-03T12:37:21Z","title":"Evolutionary $\\Gamma$-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions","external_id":{"arxiv":["2008.10962"],"isi":["000889274600001"]},"year":"2022","doi":"10.1137/21M1410968","ec_funded":1,"related_material":{"record":[{"status":"public","relation":"earlier_version","id":"10022"}]},"isi":1,"main_file_link":[{"url":" https://doi.org/10.48550/arXiv.2008.10962","open_access":"1"}]},{"page":"1815-1832","file_date_updated":"2022-01-03T11:08:31Z","publication":"Mathematische Annalen","type":"journal_article","day":"01","status":"public","intvolume":"       384","department":[{"_id":"JaMa"}],"has_accepted_license":"1","file":[{"access_level":"open_access","date_updated":"2022-01-03T11:08:31Z","file_size":410090,"file_name":"2021_MathAnn_DelloSchiavo.pdf","checksum":"2593abbf195e38efa93b6006b1e90eb1","date_created":"2022-01-03T11:08:31Z","relation":"main_file","content_type":"application/pdf","creator":"alisjak","file_id":"10596","success":1}],"date_created":"2022-01-02T23:01:35Z","article_type":"original","date_published":"2022-12-01T00:00:00Z","month":"12","language":[{"iso":"eng"}],"scopus_import":"1","publisher":"Springer Nature","article_processing_charge":"Yes (via OA deal)","oa":1,"volume":384,"date_updated":"2023-08-02T13:39:05Z","arxiv":1,"project":[{"grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425","name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020"},{"name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"quality_controlled":"1","oa_version":"Published Version","acknowledgement":"The authors are grateful to Dr. Bang-Xian Han for helpful discussions on the Sobolev-to-Lipschitz property on metric measure spaces, and to Professor Kazuhiro Kuwae, Professor Emanuel Milman, Dr. Giorgio Stefani, and Dr. Gioacchino Antonelli for reading a preliminary version of this work and for their valuable comments and suggestions. Finally, they wish to express their gratitude to two anonymous Reviewers whose suggestions improved the presentation of this work.\r\n\r\nL.D.S. gratefully acknowledges funding of his position by the Austrian Science Fund (FWF) grant F65, and by the European Research Council (ERC, grant No. 716117, awarded to Prof. Dr. Jan Maas).\r\n\r\nK.S. gratefully acknowledges funding by: the JSPS Overseas Research Fellowships, Grant Nr. 290142; World Premier International Research Center Initiative (WPI), MEXT, Japan; JSPS Grant-in-Aid for Scientific Research on Innovative Areas “Discrete Geometric Analysis for Materials Design”, Grant Number 17H06465; and the Alexander von Humboldt Stiftung, Humboldt-Forschungsstipendium.","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication_identifier":{"eissn":["1432-1807"],"issn":["0025-5831"]},"_id":"10588","citation":{"short":"L. Dello Schiavo, K. Suzuki, Mathematische Annalen 384 (2022) 1815–1832.","ista":"Dello Schiavo L, Suzuki K. 2022. Sobolev-to-Lipschitz property on QCD- spaces and applications. Mathematische Annalen. 384, 1815–1832.","ama":"Dello Schiavo L, Suzuki K. Sobolev-to-Lipschitz property on QCD- spaces and applications. <i>Mathematische Annalen</i>. 2022;384:1815-1832. doi:<a href=\"https://doi.org/10.1007/s00208-021-02331-2\">10.1007/s00208-021-02331-2</a>","mla":"Dello Schiavo, Lorenzo, and Kohei Suzuki. “Sobolev-to-Lipschitz Property on QCD- Spaces and Applications.” <i>Mathematische Annalen</i>, vol. 384, Springer Nature, 2022, pp. 1815–32, doi:<a href=\"https://doi.org/10.1007/s00208-021-02331-2\">10.1007/s00208-021-02331-2</a>.","chicago":"Dello Schiavo, Lorenzo, and Kohei Suzuki. “Sobolev-to-Lipschitz Property on QCD- Spaces and Applications.” <i>Mathematische Annalen</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s00208-021-02331-2\">https://doi.org/10.1007/s00208-021-02331-2</a>.","apa":"Dello Schiavo, L., &#38; Suzuki, K. (2022). Sobolev-to-Lipschitz property on QCD- spaces and applications. <i>Mathematische Annalen</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00208-021-02331-2\">https://doi.org/10.1007/s00208-021-02331-2</a>","ieee":"L. Dello Schiavo and K. Suzuki, “Sobolev-to-Lipschitz property on QCD- spaces and applications,” <i>Mathematische Annalen</i>, vol. 384. Springer Nature, pp. 1815–1832, 2022."},"publication_status":"published","author":[{"id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","first_name":"Lorenzo","orcid":"0000-0002-9881-6870","last_name":"Dello Schiavo","full_name":"Dello Schiavo, Lorenzo"},{"first_name":"Kohei","full_name":"Suzuki, Kohei","last_name":"Suzuki"}],"keyword":["quasi curvature-dimension condition","sub-riemannian geometry","Sobolev-to-Lipschitz property","Varadhan short-time asymptotics"],"abstract":[{"text":"We prove the Sobolev-to-Lipschitz property for metric measure spaces satisfying the quasi curvature-dimension condition recently introduced in Milman (Commun Pure Appl Math, to appear). We provide several applications to properties of the corresponding heat semigroup. In particular, under the additional assumption of infinitesimal Hilbertianity, we show the Varadhan short-time asymptotics for the heat semigroup with respect to the distance, and prove the irreducibility of the heat semigroup. These results apply in particular to large classes of (ideal) sub-Riemannian manifolds.","lang":"eng"}],"isi":1,"tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"ddc":["510"],"ec_funded":1,"doi":"10.1007/s00208-021-02331-2","year":"2022","external_id":{"isi":["000734150200001"],"arxiv":["2110.05137"]},"title":"Sobolev-to-Lipschitz property on QCD- spaces and applications"},{"page":"445-459","file_date_updated":"2023-01-26T13:02:07Z","issue":"43","publication":"Proceedings of the American Mathematical Society, Series B","type":"journal_article","day":"02","status":"public","intvolume":"         9","department":[{"_id":"JaMa"}],"has_accepted_license":"1","file":[{"file_size":326471,"file_name":"2022_ProceedingsAMS_Cremaschi.pdf","checksum":"cb4a79937c1f60d4c329a10ee797f0d2","date_created":"2023-01-26T13:02:07Z","access_level":"open_access","date_updated":"2023-01-26T13:02:07Z","success":1,"relation":"main_file","content_type":"application/pdf","creator":"dernst","file_id":"12404"}],"date_created":"2023-01-12T12:12:17Z","date_published":"2022-11-02T00:00:00Z","article_type":"original","month":"11","language":[{"iso":"eng"}],"publisher":"American Mathematical Society","scopus_import":"1","date_updated":"2023-01-26T13:04:13Z","volume":9,"oa":1,"article_processing_charge":"No","acknowledgement":"The first author was partially supported by the National Science Foundation under Grant\r\nNo. DMS-1928930 while participating in a program hosted by the Mathematical Sciences Research Institute in Berkeley, California, during the Fall 2020 semester. The second author gratefully acknowledges funding by the Austrian Science Fund (FWF) through grants F65 and ESPRIT 208, by the European Research Council (ERC, grant No. 716117, awarded to Prof. Dr. Jan Maas), and by the Deutsche Forschungsgemeinschaft through the SPP 2265.","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","project":[{"grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"},{"name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"716117"}],"oa_version":"Published Version","quality_controlled":"1","_id":"12177","publication_identifier":{"issn":["2330-1511"]},"publication_status":"published","citation":{"ieee":"T. Cremaschi and L. Dello Schiavo, “Effective contraction of Skinning maps,” <i>Proceedings of the American Mathematical Society, Series B</i>, vol. 9, no. 43. American Mathematical Society, pp. 445–459, 2022.","apa":"Cremaschi, T., &#38; Dello Schiavo, L. (2022). Effective contraction of Skinning maps. <i>Proceedings of the American Mathematical Society, Series B</i>. American Mathematical Society. <a href=\"https://doi.org/10.1090/bproc/134\">https://doi.org/10.1090/bproc/134</a>","chicago":"Cremaschi, Tommaso, and Lorenzo Dello Schiavo. “Effective Contraction of Skinning Maps.” <i>Proceedings of the American Mathematical Society, Series B</i>. American Mathematical Society, 2022. <a href=\"https://doi.org/10.1090/bproc/134\">https://doi.org/10.1090/bproc/134</a>.","ama":"Cremaschi T, Dello Schiavo L. Effective contraction of Skinning maps. <i>Proceedings of the American Mathematical Society, Series B</i>. 2022;9(43):445-459. doi:<a href=\"https://doi.org/10.1090/bproc/134\">10.1090/bproc/134</a>","mla":"Cremaschi, Tommaso, and Lorenzo Dello Schiavo. “Effective Contraction of Skinning Maps.” <i>Proceedings of the American Mathematical Society, Series B</i>, vol. 9, no. 43, American Mathematical Society, 2022, pp. 445–59, doi:<a href=\"https://doi.org/10.1090/bproc/134\">10.1090/bproc/134</a>.","short":"T. Cremaschi, L. Dello Schiavo, Proceedings of the American Mathematical Society, Series B 9 (2022) 445–459.","ista":"Cremaschi T, Dello Schiavo L. 2022. Effective contraction of Skinning maps. Proceedings of the American Mathematical Society, Series B. 9(43), 445–459."},"author":[{"last_name":"Cremaschi","full_name":"Cremaschi, Tommaso","first_name":"Tommaso"},{"orcid":"0000-0002-9881-6870","last_name":"Dello Schiavo","full_name":"Dello Schiavo, Lorenzo","first_name":"Lorenzo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E"}],"abstract":[{"lang":"eng","text":"Using elementary hyperbolic geometry, we give an explicit formula for the contraction constant of the skinning map over moduli spaces of relatively acylindrical hyperbolic manifolds."}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","image":"/images/cc_by_nc_nd.png","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","short":"CC BY-NC-ND (4.0)"},"ddc":["510"],"ec_funded":1,"year":"2022","doi":"10.1090/bproc/134","title":"Effective contraction of Skinning maps"},{"article_type":"original","date_published":"2021-08-25T00:00:00Z","month":"08","language":[{"iso":"eng"}],"publisher":"World Scientific","scopus_import":"1","department":[{"_id":"JuFi"}],"date_created":"2021-09-12T22:01:25Z","type":"journal_article","day":"25","status":"public","intvolume":"        31","issue":"09","publication":"Mathematical Models and Methods in Applied Sciences","year":"2021","doi":"10.1142/S0218202521500457","title":"On nonlinear problems of parabolic type with implicit constitutive equations involving flux","external_id":{"arxiv":["2009.06917"],"isi":["000722222900004"]},"main_file_link":[{"url":"https://arxiv.org/abs/2009.06917","open_access":"1"}],"isi":1,"publication_status":"published","citation":{"mla":"Bulíček, Miroslav, et al. “On Nonlinear Problems of Parabolic Type with Implicit Constitutive Equations Involving Flux.” <i>Mathematical Models and Methods in Applied Sciences</i>, vol. 31, no. 09, World Scientific, 2021, doi:<a href=\"https://doi.org/10.1142/S0218202521500457\">10.1142/S0218202521500457</a>.","ama":"Bulíček M, Maringová E, Málek J. On nonlinear problems of parabolic type with implicit constitutive equations involving flux. <i>Mathematical Models and Methods in Applied Sciences</i>. 2021;31(09). doi:<a href=\"https://doi.org/10.1142/S0218202521500457\">10.1142/S0218202521500457</a>","ista":"Bulíček M, Maringová E, Málek J. 2021. On nonlinear problems of parabolic type with implicit constitutive equations involving flux. Mathematical Models and Methods in Applied Sciences. 31(09).","short":"M. Bulíček, E. Maringová, J. Málek, Mathematical Models and Methods in Applied Sciences 31 (2021).","apa":"Bulíček, M., Maringová, E., &#38; Málek, J. (2021). On nonlinear problems of parabolic type with implicit constitutive equations involving flux. <i>Mathematical Models and Methods in Applied Sciences</i>. World Scientific. <a href=\"https://doi.org/10.1142/S0218202521500457\">https://doi.org/10.1142/S0218202521500457</a>","ieee":"M. Bulíček, E. Maringová, and J. Málek, “On nonlinear problems of parabolic type with implicit constitutive equations involving flux,” <i>Mathematical Models and Methods in Applied Sciences</i>, vol. 31, no. 09. World Scientific, 2021.","chicago":"Bulíček, Miroslav, Erika Maringová, and Josef Málek. “On Nonlinear Problems of Parabolic Type with Implicit Constitutive Equations Involving Flux.” <i>Mathematical Models and Methods in Applied Sciences</i>. World Scientific, 2021. <a href=\"https://doi.org/10.1142/S0218202521500457\">https://doi.org/10.1142/S0218202521500457</a>."},"keyword":["Nonlinear parabolic systems","implicit constitutive theory","weak solutions","existence","uniqueness"],"author":[{"last_name":"Bulíček","full_name":"Bulíček, Miroslav","first_name":"Miroslav"},{"id":"dbabca31-66eb-11eb-963a-fb9c22c880b4","full_name":"Maringová, Erika","last_name":"Maringová","first_name":"Erika"},{"first_name":"Josef","last_name":"Málek","full_name":"Málek, Josef"}],"abstract":[{"text":"We study systems of nonlinear partial differential equations of parabolic type, in which the elliptic operator is replaced by the first-order divergence operator acting on a flux function, which is related to the spatial gradient of the unknown through an additional implicit equation. This setting, broad enough in terms of applications, significantly expands the paradigm of nonlinear parabolic problems. Formulating four conditions concerning the form of the implicit equation, we first show that these conditions describe a maximal monotone p-coercive graph. We then establish the global-in-time and large-data existence of a (weak) solution and its uniqueness. To this end, we adopt and significantly generalize Minty’s method of monotone mappings. A unified theory, containing several novel tools, is developed in a way to be tractable from the point of view of numerical approximations.","lang":"eng"}],"oa":1,"date_updated":"2023-09-04T11:43:45Z","volume":31,"article_processing_charge":"No","arxiv":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","acknowledgement":"M. Bulíček and J. Málek acknowledge the support of the project No. 18-12719S financed by the Czech\r\nScience foundation (GAČR). E. Maringová acknowledges support from Charles University Research program \r\nUNCE/SCI/023, the grant SVV-2020-260583 by the Ministry of Education, Youth and Sports, Czech Republic\r\nand from the Austrian Science Fund (FWF), grants P30000, W1245, and F65. M. Bulíček and J. Málek are\r\nmembers of the Nečas Center for Mathematical Modelling.\r\n","oa_version":"Preprint","quality_controlled":"1","project":[{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504"}],"_id":"10005","publication_identifier":{"eissn":["1793-6314"],"issn":["0218-2025"]}},{"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2005.14177"}],"ec_funded":1,"doi":"10.4310/CIS.2021.v21.n4.a1","year":"2021","external_id":{"arxiv":["2005.14177"]},"title":"Trajectorial dissipation and gradient flow for the relative entropy in Markov chains","article_processing_charge":"No","date_updated":"2021-09-20T12:51:18Z","volume":21,"oa":1,"arxiv":1,"oa_version":"Preprint","project":[{"grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425","name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020"},{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504"}],"quality_controlled":"1","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","acknowledgement":"I.K. acknowledges support from the U.S. National Science Foundation under Grant NSF-DMS-20-04997. J.M. acknowledges support from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 716117) and from the Austrian Science Fund (FWF) through project F65. W.S. acknowledges support from the Austrian Science Fund (FWF) under grant P28861 and by the Vienna Science and Technology Fund (WWTF) through projects MA14-008 and MA16-021.","publication_identifier":{"issn":["1526-7555"]},"_id":"10023","citation":{"apa":"Karatzas, I., Maas, J., &#38; Schachermayer, W. (2021). Trajectorial dissipation and gradient flow for the relative entropy in Markov chains. <i>Communications in Information and Systems</i>. International Press. <a href=\"https://doi.org/10.4310/CIS.2021.v21.n4.a1\">https://doi.org/10.4310/CIS.2021.v21.n4.a1</a>","ieee":"I. Karatzas, J. Maas, and W. Schachermayer, “Trajectorial dissipation and gradient flow for the relative entropy in Markov chains,” <i>Communications in Information and Systems</i>, vol. 21, no. 4. International Press, pp. 481–536, 2021.","chicago":"Karatzas, Ioannis, Jan Maas, and Walter Schachermayer. “Trajectorial Dissipation and Gradient Flow for the Relative Entropy in Markov Chains.” <i>Communications in Information and Systems</i>. International Press, 2021. <a href=\"https://doi.org/10.4310/CIS.2021.v21.n4.a1\">https://doi.org/10.4310/CIS.2021.v21.n4.a1</a>.","mla":"Karatzas, Ioannis, et al. “Trajectorial Dissipation and Gradient Flow for the Relative Entropy in Markov Chains.” <i>Communications in Information and Systems</i>, vol. 21, no. 4, International Press, 2021, pp. 481–536, doi:<a href=\"https://doi.org/10.4310/CIS.2021.v21.n4.a1\">10.4310/CIS.2021.v21.n4.a1</a>.","ama":"Karatzas I, Maas J, Schachermayer W. Trajectorial dissipation and gradient flow for the relative entropy in Markov chains. <i>Communications in Information and Systems</i>. 2021;21(4):481-536. doi:<a href=\"https://doi.org/10.4310/CIS.2021.v21.n4.a1\">10.4310/CIS.2021.v21.n4.a1</a>","ista":"Karatzas I, Maas J, Schachermayer W. 2021. Trajectorial dissipation and gradient flow for the relative entropy in Markov chains. Communications in Information and Systems. 21(4), 481–536.","short":"I. Karatzas, J. Maas, W. Schachermayer, Communications in Information and Systems 21 (2021) 481–536."},"publication_status":"published","author":[{"first_name":"Ioannis","last_name":"Karatzas","full_name":"Karatzas, Ioannis"},{"id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","first_name":"Jan","orcid":"0000-0002-0845-1338","last_name":"Maas","full_name":"Maas, Jan"},{"last_name":"Schachermayer","full_name":"Schachermayer, Walter","first_name":"Walter"}],"keyword":["Markov Chain","relative entropy","time reversal","steepest descent","gradient flow"],"abstract":[{"text":"We study the temporal dissipation of variance and relative entropy for ergodic Markov Chains in continuous time, and compute explicitly the corresponding dissipation rates. These are identified, as is well known, in the case of the variance in terms of an appropriate Hilbertian norm; and in the case of the relative entropy, in terms of a Dirichlet form which morphs into a version of the familiar Fisher information under conditions of detailed balance. Here we obtain trajectorial versions of these results, valid along almost every path of the random motion and most transparent in the backwards direction of time. Martingale arguments and time reversal play crucial roles, as in the recent work of Karatzas, Schachermayer and Tschiderer for conservative diffusions. Extensions are developed to general “convex divergences” and to countable state-spaces. The steepest descent and gradient flow properties for the variance, the relative entropy, and appropriate generalizations, are studied along with their respective geometries under conditions of detailed balance, leading to a very direct proof for the HWI inequality of Otto and Villani in the present context.","lang":"eng"}],"department":[{"_id":"JaMa"}],"date_created":"2021-09-19T08:53:19Z","date_published":"2021-06-04T00:00:00Z","article_type":"original","month":"06","language":[{"iso":"eng"}],"publisher":"International Press","page":"481-536","publication":"Communications in Information and Systems","issue":"4","type":"journal_article","day":"04","status":"public","intvolume":"        21"},{"author":[{"last_name":"Portinale","full_name":"Portinale, Lorenzo","first_name":"Lorenzo","id":"30AD2CBC-F248-11E8-B48F-1D18A9856A87"}],"abstract":[{"lang":"eng","text":"This PhD thesis is primarily focused on the study of discrete transport problems, introduced for the first time in the seminal works of Maas [Maa11] and Mielke [Mie11] on finite state Markov chains and reaction-diffusion equations, respectively. More in detail, my research focuses on the study of transport costs on graphs, in particular the convergence and the stability of such problems in the discrete-to-continuum limit. This thesis also includes some results concerning\r\nnon-commutative optimal transport. The first chapter of this thesis consists of a general introduction to the optimal transport problems, both in the discrete, the continuous, and the non-commutative setting. Chapters 2 and 3 present the content of two works, obtained in collaboration with Peter Gladbach, Eva Kopfer, and Jan Maas, where we have been able to show the convergence of discrete transport costs on periodic graphs to suitable continuous ones, which can be described by means of a homogenisation result. We first focus on the particular case of quadratic costs on the real line and then extending the result to more general costs in arbitrary dimension. Our results are the first complete characterisation of limits of transport costs on periodic graphs in arbitrary dimension which do not rely on any additional symmetry. In Chapter 4 we turn our attention to one of the intriguing connection between evolution equations and optimal transport, represented by the theory of gradient flows. We show that discrete gradient flow structures associated to a finite volume approximation of a certain class of diffusive equations (Fokker–Planck) is stable in the limit of vanishing meshes, reproving the convergence of the scheme via the method of evolutionary Γ-convergence and exploiting a more variational point of view on the problem. This is based on a collaboration with Dominik Forkert and Jan Maas. Chapter 5 represents a change of perspective, moving away from the discrete world and reaching the non-commutative one. As in the discrete case, we discuss how classical tools coming from the commutative optimal transport can be translated into the setting of density matrices. In particular, in this final chapter we present a non-commutative version of the Schrödinger problem (or entropic regularised optimal transport problem) and discuss existence and characterisation of minimisers, a duality result, and present a non-commutative version of the well-known Sinkhorn algorithm to compute the above mentioned optimisers. This is based on a joint work with Dario Feliciangeli and Augusto Gerolin. Finally, Appendix A and B contain some additional material and discussions, with particular attention to Harnack inequalities and the regularity of flows on discrete spaces."}],"publication_status":"published","citation":{"ista":"Portinale L. 2021. Discrete-to-continuum limits of transport problems and gradient flows in the space of measures. Institute of Science and Technology Austria.","short":"L. Portinale, Discrete-to-Continuum Limits of Transport Problems and Gradient Flows in the Space of Measures, Institute of Science and Technology Austria, 2021.","mla":"Portinale, Lorenzo. <i>Discrete-to-Continuum Limits of Transport Problems and Gradient Flows in the Space of Measures</i>. Institute of Science and Technology Austria, 2021, doi:<a href=\"https://doi.org/10.15479/at:ista:10030\">10.15479/at:ista:10030</a>.","ama":"Portinale L. Discrete-to-continuum limits of transport problems and gradient flows in the space of measures. 2021. doi:<a href=\"https://doi.org/10.15479/at:ista:10030\">10.15479/at:ista:10030</a>","chicago":"Portinale, Lorenzo. “Discrete-to-Continuum Limits of Transport Problems and Gradient Flows in the Space of Measures.” Institute of Science and Technology Austria, 2021. <a href=\"https://doi.org/10.15479/at:ista:10030\">https://doi.org/10.15479/at:ista:10030</a>.","apa":"Portinale, L. (2021). <i>Discrete-to-continuum limits of transport problems and gradient flows in the space of measures</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/at:ista:10030\">https://doi.org/10.15479/at:ista:10030</a>","ieee":"L. Portinale, “Discrete-to-continuum limits of transport problems and gradient flows in the space of measures,” Institute of Science and Technology Austria, 2021."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","acknowledgement":"The author gratefully acknowledges support by the Austrian Science Fund (FWF), grants No W1245.","project":[{"call_identifier":"FWF","_id":"260788DE-B435-11E9-9278-68D0E5697425","name":"Dissipation and Dispersion in Nonlinear Partial Differential Equations"},{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504"}],"oa_version":"Published Version","_id":"10030","publication_identifier":{"issn":["2663-337X"]},"oa":1,"date_updated":"2023-09-07T13:31:06Z","article_processing_charge":"No","title":"Discrete-to-continuum limits of transport problems and gradient flows in the space of measures","acknowledged_ssus":[{"_id":"M-Shop"},{"_id":"NanoFab"}],"year":"2021","doi":"10.15479/at:ista:10030","ddc":["515"],"related_material":{"record":[{"status":"public","relation":"part_of_dissertation","id":"10022"},{"status":"public","relation":"part_of_dissertation","id":"9792"},{"id":"7573","relation":"part_of_dissertation","status":"public"}]},"alternative_title":["ISTA Thesis"],"tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"supervisor":[{"orcid":"0000-0002-0845-1338","last_name":"Maas","full_name":"Maas, Jan","first_name":"Jan","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87"}],"status":"public","type":"dissertation","day":"22","file_date_updated":"2022-03-10T12:14:42Z","language":[{"iso":"eng"}],"publisher":"Institute of Science and Technology Austria","date_published":"2021-09-22T00:00:00Z","month":"09","file":[{"content_type":"application/x-zip-compressed","relation":"source_file","file_id":"10032","creator":"cchlebak","date_updated":"2022-03-10T12:14:42Z","access_level":"closed","file_name":"tex_and_pictures.zip","file_size":3876668,"date_created":"2021-09-21T09:17:34Z","checksum":"8cd60dcb8762e8f21867e21e8001e183"},{"access_level":"open_access","date_updated":"2021-09-27T11:14:31Z","file_size":2532673,"file_name":"thesis_portinale_Final (1).pdf","checksum":"9789e9d967c853c1503ec7f307170279","date_created":"2021-09-27T11:14:31Z","relation":"main_file","content_type":"application/pdf","creator":"cchlebak","file_id":"10047"}],"date_created":"2021-09-21T09:14:15Z","department":[{"_id":"GradSch"},{"_id":"JaMa"}],"degree_awarded":"PhD","has_accepted_license":"1"},{"year":"2021","doi":"10.1016/j.jfa.2021.109234","ec_funded":1,"title":"Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local Dirichlet spaces","external_id":{"isi":["000703896600005"],"arxiv":["2008.01492"]},"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2008.01492"}],"article_number":"109234","isi":1,"citation":{"apa":"Dello Schiavo, L., &#38; Suzuki, K. (2021). Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local Dirichlet spaces. <i>Journal of Functional Analysis</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jfa.2021.109234\">https://doi.org/10.1016/j.jfa.2021.109234</a>","ieee":"L. Dello Schiavo and K. Suzuki, “Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local Dirichlet spaces,” <i>Journal of Functional Analysis</i>, vol. 281, no. 11. Elsevier, 2021.","chicago":"Dello Schiavo, Lorenzo, and Kohei Suzuki. “Rademacher-Type Theorems and Sobolev-to-Lipschitz Properties for Strongly Local Dirichlet Spaces.” <i>Journal of Functional Analysis</i>. Elsevier, 2021. <a href=\"https://doi.org/10.1016/j.jfa.2021.109234\">https://doi.org/10.1016/j.jfa.2021.109234</a>.","ama":"Dello Schiavo L, Suzuki K. Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local Dirichlet spaces. <i>Journal of Functional Analysis</i>. 2021;281(11). doi:<a href=\"https://doi.org/10.1016/j.jfa.2021.109234\">10.1016/j.jfa.2021.109234</a>","mla":"Dello Schiavo, Lorenzo, and Kohei Suzuki. “Rademacher-Type Theorems and Sobolev-to-Lipschitz Properties for Strongly Local Dirichlet Spaces.” <i>Journal of Functional Analysis</i>, vol. 281, no. 11, 109234, Elsevier, 2021, doi:<a href=\"https://doi.org/10.1016/j.jfa.2021.109234\">10.1016/j.jfa.2021.109234</a>.","ista":"Dello Schiavo L, Suzuki K. 2021. Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local Dirichlet spaces. Journal of Functional Analysis. 281(11), 109234.","short":"L. Dello Schiavo, K. Suzuki, Journal of Functional Analysis 281 (2021)."},"publication_status":"published","abstract":[{"lang":"eng","text":"We extensively discuss the Rademacher and Sobolev-to-Lipschitz properties for generalized intrinsic distances on strongly local Dirichlet spaces possibly without square field operator. We present many non-smooth and infinite-dimensional examples. As an application, we prove the integral Varadhan short-time asymptotic with respect to a given distance function for a large class of strongly local Dirichlet forms."}],"author":[{"id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","first_name":"Lorenzo","orcid":"0000-0002-9881-6870","last_name":"Dello Schiavo","full_name":"Dello Schiavo, Lorenzo"},{"last_name":"Suzuki","full_name":"Suzuki, Kohei","first_name":"Kohei"}],"arxiv":1,"article_processing_charge":"No","oa":1,"date_updated":"2023-08-14T07:05:44Z","volume":281,"publication_identifier":{"eissn":["1096-0783"],"issn":["0022-1236"]},"_id":"10070","oa_version":"Preprint","project":[{"grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems"},{"grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425","name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020"}],"quality_controlled":"1","acknowledgement":"The authors are grateful to Professor Kazuhiro Kuwae for kindly providing a copy of [49]. They are also grateful to Dr. Bang-Xian Han for helpful discussions on the Sobolev-to-Lipschitz property on metric measure spaces. They wish to express their deepest gratitude to an anonymous Reviewer, whose punctual remarks and comments greatly improved the accessibility and overall quality of the initial submission. This work was completed while L.D.S. was a member of the Institut für Angewandte Mathematik of the University of Bonn. He acknowledges funding of his position at that time by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through the Sonderforschungsbereich (Sfb, Collaborative Research Center) 1060 - project number 211504053. He also acknowledges funding of his current position by the Austrian Science Fund (FWF) grant F65, and by the European Research Council (ERC, grant No. 716117, awarded to Prof. Dr. Jan Maas). K.S. gratefully acknowledges funding by: the JSPS Overseas Research Fellowships, Grant Nr. 290142; World Premier International Research Center Initiative (WPI), MEXT, Japan; and JSPS Grant-in-Aid for Scientific Research on Innovative Areas “Discrete Geometric Analysis for Materials Design”, Grant Number 17H06465.","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","month":"09","article_type":"original","date_published":"2021-09-15T00:00:00Z","scopus_import":"1","publisher":"Elsevier","language":[{"iso":"eng"}],"department":[{"_id":"JaMa"}],"date_created":"2021-10-03T22:01:21Z","day":"15","type":"journal_article","intvolume":"       281","status":"public","publication":"Journal of Functional Analysis","issue":"11"},{"has_accepted_license":"1","department":[{"_id":"JuFi"}],"file":[{"success":1,"file_id":"11385","creator":"dernst","relation":"main_file","content_type":"application/pdf","checksum":"8c0a9396335f0b70e1f5cbfe450a987a","date_created":"2022-05-16T10:55:45Z","file_size":795483,"file_name":"2021_MathModelsMethods_Abbatiello.pdf","access_level":"open_access","date_updated":"2022-05-16T10:55:45Z"}],"date_created":"2021-12-26T23:01:27Z","month":"10","date_published":"2021-10-13T00:00:00Z","article_type":"original","publisher":"World Scientific Publishing","scopus_import":"1","language":[{"iso":"eng"}],"issue":"11","publication":"Mathematical Models and Methods in Applied Sciences","page":"2165-2212","file_date_updated":"2022-05-16T10:55:45Z","day":"13","type":"journal_article","intvolume":"        31","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","image":"/images/cc_by_nc_nd.png","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","short":"CC BY-NC-ND (4.0)"},"isi":1,"ddc":["510"],"doi":"10.1142/S0218202521500470","year":"2021","title":"On the dynamic slip boundary condition for Navier-Stokes-like problems","external_id":{"isi":["000722309400001"],"arxiv":["2009.09057"]},"arxiv":1,"date_updated":"2023-08-17T06:29:01Z","volume":31,"oa":1,"article_processing_charge":"No","_id":"10575","publication_identifier":{"eissn":["1793-6314"],"issn":["0218-2025"]},"acknowledgement":"The research of A. Abbatiello is supported by Einstein Foundation, Berlin. A. Abbatiello is also member of the Italian National Group for the Mathematical Physics (GNFM) of INdAM. M. Bulíček acknowledges the support of the project No. 20-11027X financed by Czech Science Foundation (GACR). M. Bulíček is member of the Jindřich Nečas Center for Mathematical Modelling. E. Maringová acknowledges support from Charles University Research program UNCE/SCI/023, the grant SVV-2020-260583 by the Ministry of Education, Youth and Sports, Czech Republic and from the Austrian Science Fund (FWF), grants P30000, W1245, and F65.","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa_version":"Published Version","project":[{"grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems"},{"call_identifier":"FWF","_id":"260788DE-B435-11E9-9278-68D0E5697425","name":"Dissipation and Dispersion in Nonlinear Partial Differential Equations"}],"quality_controlled":"1","publication_status":"published","citation":{"mla":"Abbatiello, Anna, et al. “On the Dynamic Slip Boundary Condition for Navier-Stokes-like Problems.” <i>Mathematical Models and Methods in Applied Sciences</i>, vol. 31, no. 11, World Scientific Publishing, 2021, pp. 2165–212, doi:<a href=\"https://doi.org/10.1142/S0218202521500470\">10.1142/S0218202521500470</a>.","ama":"Abbatiello A, Bulíček M, Maringová E. On the dynamic slip boundary condition for Navier-Stokes-like problems. <i>Mathematical Models and Methods in Applied Sciences</i>. 2021;31(11):2165-2212. doi:<a href=\"https://doi.org/10.1142/S0218202521500470\">10.1142/S0218202521500470</a>","ista":"Abbatiello A, Bulíček M, Maringová E. 2021. On the dynamic slip boundary condition for Navier-Stokes-like problems. Mathematical Models and Methods in Applied Sciences. 31(11), 2165–2212.","short":"A. Abbatiello, M. Bulíček, E. Maringová, Mathematical Models and Methods in Applied Sciences 31 (2021) 2165–2212.","ieee":"A. Abbatiello, M. Bulíček, and E. Maringová, “On the dynamic slip boundary condition for Navier-Stokes-like problems,” <i>Mathematical Models and Methods in Applied Sciences</i>, vol. 31, no. 11. World Scientific Publishing, pp. 2165–2212, 2021.","apa":"Abbatiello, A., Bulíček, M., &#38; Maringová, E. (2021). On the dynamic slip boundary condition for Navier-Stokes-like problems. <i>Mathematical Models and Methods in Applied Sciences</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/S0218202521500470\">https://doi.org/10.1142/S0218202521500470</a>","chicago":"Abbatiello, Anna, Miroslav Bulíček, and Erika Maringová. “On the Dynamic Slip Boundary Condition for Navier-Stokes-like Problems.” <i>Mathematical Models and Methods in Applied Sciences</i>. World Scientific Publishing, 2021. <a href=\"https://doi.org/10.1142/S0218202521500470\">https://doi.org/10.1142/S0218202521500470</a>."},"abstract":[{"lang":"eng","text":"The choice of the boundary conditions in mechanical problems has to reflect the interaction of the considered material with the surface. Still the assumption of the no-slip condition is preferred in order to avoid boundary terms in the analysis and slipping effects are usually overlooked. Besides the “static slip models”, there are phenomena that are not accurately described by them, e.g. at the moment when the slip changes rapidly, the wall shear stress and the slip can exhibit a sudden overshoot and subsequent relaxation. When these effects become significant, the so-called dynamic slip phenomenon occurs. We develop a mathematical analysis of Navier–Stokes-like problems with a dynamic slip boundary condition, which requires a proper generalization of the Gelfand triplet and the corresponding function space setting."}],"author":[{"first_name":"Anna","last_name":"Abbatiello","full_name":"Abbatiello, Anna"},{"last_name":"Bulíček","full_name":"Bulíček, Miroslav","first_name":"Miroslav"},{"first_name":"Erika","last_name":"Maringová","full_name":"Maringová, Erika","id":"dbabca31-66eb-11eb-963a-fb9c22c880b4"}]}]