[{"project":[{"name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504"}],"type":"journal_article","status":"public","date_published":"2024-01-26T00:00:00Z","publisher":"Springer Nature","quality_controlled":"1","department":[{"_id":"JaMa"}],"publication_status":"epub_ahead","author":[{"orcid":"0000-0002-9881-6870","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","last_name":"Dello Schiavo","full_name":"Dello Schiavo, Lorenzo","first_name":"Lorenzo"},{"last_name":"Kopfer","full_name":"Kopfer, Eva","first_name":"Eva"},{"first_name":"Karl Theodor","full_name":"Sturm, Karl Theodor","last_name":"Sturm"}],"month":"01","publication_identifier":{"issn":["0926-2601"],"eissn":["1572-929X"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","abstract":[{"lang":"eng","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."}],"day":"26","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1007/s11118-023-10118-0"}],"oa_version":"Published Version","language":[{"iso":"eng"}],"_id":"14934","article_type":"original","publication":"Potential Analysis","doi":"10.1007/s11118-023-10118-0","article_processing_charge":"Yes (via OA deal)","year":"2024","oa":1,"date_updated":"2024-02-05T13:04:23Z","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.","date_created":"2024-02-04T23:00:54Z","title":"A discovery tour in random Riemannian geometry","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>.","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>.","ista":"Dello Schiavo L, Kopfer E, Sturm KT. 2024. A discovery tour in random Riemannian geometry. Potential Analysis.","ieee":"L. Dello Schiavo, E. Kopfer, and K. T. Sturm, “A discovery tour in random Riemannian geometry,” <i>Potential Analysis</i>. Springer Nature, 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>","short":"L. Dello Schiavo, E. Kopfer, K.T. Sturm, Potential Analysis (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>"},"scopus_import":"1"},{"status":"public","type":"journal_article","arxiv":1,"author":[{"orcid":"0000-0003-0754-8530","last_name":"Feliciangeli","id":"41A639AA-F248-11E8-B48F-1D18A9856A87","full_name":"Feliciangeli, Dario","first_name":"Dario"},{"last_name":"Gerolin","first_name":"Augusto","full_name":"Gerolin, Augusto"},{"full_name":"Portinale, Lorenzo","first_name":"Lorenzo","id":"30AD2CBC-F248-11E8-B48F-1D18A9856A87","last_name":"Portinale"}],"month":"08","publication_identifier":{"eissn":["1096-0783"],"issn":["0022-1236"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2106.11217"}],"oa_version":"Preprint","day":"15","language":[{"iso":"eng"}],"publication":"Journal of Functional Analysis","article_processing_charge":"No","issue":"4","oa":1,"date_updated":"2023-11-14T13:21:01Z","title":"A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature","isi":1,"scopus_import":"1","intvolume":"       285","project":[{"name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020","grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425"},{"call_identifier":"H2020","name":"Analysis of quantum many-body systems","grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"},{"name":"Taming Complexity in Partial Di erential Systems","call_identifier":"FWF","grant_number":" F06504","_id":"260482E2-B435-11E9-9278-68D0E5697425"}],"date_published":"2023-08-15T00:00:00Z","publisher":"Elsevier","quality_controlled":"1","volume":285,"department":[{"_id":"RoSe"},{"_id":"JaMa"}],"publication_status":"published","abstract":[{"text":"This paper establishes new connections between many-body quantum systems, One-body Reduced Density Matrices Functional Theory (1RDMFT) and Optimal Transport (OT), by interpreting the problem of computing the ground-state energy of a finite-dimensional composite quantum system at positive temperature as a non-commutative entropy regularized Optimal Transport problem. We develop a new approach to fully characterize the dual-primal solutions in such non-commutative setting. The mathematical formalism is particularly relevant in quantum chemistry: numerical realizations of the many-electron ground-state energy can be computed via a non-commutative version of Sinkhorn algorithm. Our approach allows to prove convergence and robustness of this algorithm, which, to our best knowledge, were unknown even in the two marginal case. Our methods are based on a priori estimates in the dual problem, which we believe to be of independent interest. Finally, the above results are extended in 1RDMFT setting, where bosonic or fermionic symmetry conditions are enforced on the problem.","lang":"eng"}],"external_id":{"arxiv":["2106.11217"],"isi":["000990804300001"]},"_id":"12911","article_type":"original","doi":"10.1016/j.jfa.2023.109963","year":"2023","acknowledgement":"This work started when A.G. was visiting the Erwin Schrödinger Institute and then continued when D.F. and L.P visited the Theoretical Chemistry Department of the Vrije Universiteit Amsterdam. The authors thank the hospitality of both places and, especially, P. Gori-Giorgi and K. Giesbertz for fruitful discussions and literature suggestions in the early state of the project. The authors also thank J. Maas and R. Seiringer for their feedback and useful comments to a first draft of the article. Finally, we acknowledge the high quality review done by the anonymous referee of our paper, who we would like to thank for the excellent work and constructive feedback.\r\nD.F acknowledges support by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreements No 716117 and No 694227). A.G. acknowledges funding by the HORIZON EUROPE European Research Council under H2020/MSCA-IF “OTmeetsDFT” [grant ID: 795942] as well as partial support of his research by the Canada Research Chairs Program (ID 2021-00234) and Natural Sciences and Engineering Research Council of Canada, RGPIN-2022-05207. L.P. acknowledges support by the Austrian Science Fund (FWF), grants No W1245 and No F65, and by the Deutsche Forschungsgemeinschaft (DFG) - Project number 390685813.","date_created":"2023-05-07T22:01:02Z","citation":{"ieee":"D. Feliciangeli, A. Gerolin, and L. Portinale, “A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature,” <i>Journal of Functional Analysis</i>, vol. 285, no. 4. Elsevier, 2023.","ama":"Feliciangeli D, Gerolin A, Portinale L. A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature. <i>Journal of Functional Analysis</i>. 2023;285(4). doi:<a href=\"https://doi.org/10.1016/j.jfa.2023.109963\">10.1016/j.jfa.2023.109963</a>","short":"D. Feliciangeli, A. Gerolin, L. Portinale, Journal of Functional Analysis 285 (2023).","chicago":"Feliciangeli, Dario, Augusto Gerolin, and Lorenzo Portinale. “A Non-Commutative Entropic Optimal Transport Approach to Quantum Composite Systems at Positive Temperature.” <i>Journal of Functional Analysis</i>. Elsevier, 2023. <a href=\"https://doi.org/10.1016/j.jfa.2023.109963\">https://doi.org/10.1016/j.jfa.2023.109963</a>.","mla":"Feliciangeli, Dario, et al. “A Non-Commutative Entropic Optimal Transport Approach to Quantum Composite Systems at Positive Temperature.” <i>Journal of Functional Analysis</i>, vol. 285, no. 4, 109963, Elsevier, 2023, doi:<a href=\"https://doi.org/10.1016/j.jfa.2023.109963\">10.1016/j.jfa.2023.109963</a>.","ista":"Feliciangeli D, Gerolin A, Portinale L. 2023. A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature. Journal of Functional Analysis. 285(4), 109963.","apa":"Feliciangeli, D., Gerolin, A., &#38; Portinale, L. (2023). A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature. <i>Journal of Functional Analysis</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jfa.2023.109963\">https://doi.org/10.1016/j.jfa.2023.109963</a>"},"related_material":{"record":[{"status":"public","id":"9792","relation":"earlier_version"}]},"article_number":"109963","ec_funded":1},{"title":"Homogenisation of dynamical optimal transport on periodic graphs","article_processing_charge":"Yes (via OA deal)","issue":"5","date_updated":"2023-10-04T11:34:49Z","oa":1,"scopus_import":"1","intvolume":"        62","has_accepted_license":"1","isi":1,"language":[{"iso":"eng"}],"publication":"Calculus of Variations and Partial Differential Equations","arxiv":1,"author":[{"first_name":"Peter","full_name":"Gladbach, Peter","last_name":"Gladbach"},{"last_name":"Kopfer","full_name":"Kopfer, Eva","first_name":"Eva"},{"last_name":"Maas","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-0845-1338","first_name":"Jan","full_name":"Maas, Jan"},{"full_name":"Portinale, Lorenzo","first_name":"Lorenzo","id":"30AD2CBC-F248-11E8-B48F-1D18A9856A87","last_name":"Portinale"}],"file":[{"creator":"dernst","file_size":1240995,"access_level":"open_access","relation":"main_file","content_type":"application/pdf","success":1,"file_id":"14393","checksum":"359bee38d94b7e0aa73925063cb8884d","file_name":"2023_CalculusEquations_Gladbach.pdf","date_created":"2023-10-04T11:34:10Z","date_updated":"2023-10-04T11:34:10Z"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Published Version","day":"28","month":"04","publication_identifier":{"issn":["0944-2669"],"eissn":["1432-0835"]},"type":"journal_article","status":"public","date_created":"2023-05-14T22:01:00Z","citation":{"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>","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.","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>.","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>.","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.","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>","short":"P. Gladbach, E. Kopfer, J. Maas, L. Portinale, Calculus of Variations and Partial Differential Equations 62 (2023)."},"year":"2023","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).","article_number":"143","ec_funded":1,"article_type":"original","_id":"12959","file_date_updated":"2023-10-04T11:34:10Z","doi":"10.1007/s00526-023-02472-z","publication_status":"published","abstract":[{"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.","lang":"eng"}],"external_id":{"isi":["000980588900001"],"arxiv":["2110.15321"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"ddc":["510"],"project":[{"grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics"},{"name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"},{"call_identifier":"FWF","name":"Dissipation and Dispersion in Nonlinear Partial Differential Equations","_id":"260788DE-B435-11E9-9278-68D0E5697425"}],"volume":62,"quality_controlled":"1","department":[{"_id":"JaMa"}],"date_published":"2023-04-28T00:00:00Z","publisher":"Springer Nature"},{"month":"05","publication_identifier":{"eissn":["1083-589X"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file":[{"relation":"main_file","access_level":"open_access","content_type":"application/pdf","file_size":271434,"creator":"dernst","date_updated":"2023-06-19T09:37:40Z","date_created":"2023-06-19T09:37:40Z","file_id":"13152","checksum":"4a543fe4b3f9e747cc52167c17bfb524","file_name":"2023_ElectronCommProbability_Schiavo.pdf","success":1}],"oa_version":"Published Version","day":"05","author":[{"full_name":"Dello Schiavo, Lorenzo","first_name":"Lorenzo","orcid":"0000-0002-9881-6870","last_name":"Dello Schiavo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E"},{"full_name":"Lytvynov, Eugene","first_name":"Eugene","last_name":"Lytvynov"}],"type":"journal_article","status":"public","isi":1,"scopus_import":"1","has_accepted_license":"1","intvolume":"        28","article_processing_charge":"No","oa":1,"date_updated":"2023-12-13T11:24:57Z","title":"A Mecke-type characterization of the Dirichlet–Ferguson measure","publication":"Electronic Communications in Probability","language":[{"iso":"eng"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"ddc":["510"],"abstract":[{"text":"We prove a characterization of the Dirichlet–Ferguson measure over an arbitrary finite diffuse measure space. We provide an interpretation of this characterization in analogy with the Mecke identity for Poisson point processes.","lang":"eng"}],"external_id":{"isi":["001042025400001"]},"publication_status":"published","date_published":"2023-05-05T00:00:00Z","publisher":"Institute of Mathematical Statistics","quality_controlled":"1","volume":28,"page":"1-12","department":[{"_id":"JaMa"}],"project":[{"name":"Configuration Spaces over Non-Smooth Spaces","_id":"34dbf174-11ca-11ed-8bc3-afe9d43d4b9c","grant_number":"E208"}],"year":"2023","acknowledgement":"Research supported by the Sfb 1060 The Mathematics of Emergent Effects (University of Bonn). L.D.S. gratefully acknowledges funding of his current position by the Austrian Science Fund (FWF) through project ESPRIT 208.","citation":{"short":"L. Dello Schiavo, E. Lytvynov, Electronic Communications in Probability 28 (2023) 1–12.","ama":"Dello Schiavo L, Lytvynov E. A Mecke-type characterization of the Dirichlet–Ferguson measure. <i>Electronic Communications in Probability</i>. 2023;28:1-12. doi:<a href=\"https://doi.org/10.1214/23-ECP528\">10.1214/23-ECP528</a>","ieee":"L. Dello Schiavo and E. Lytvynov, “A Mecke-type characterization of the Dirichlet–Ferguson measure,” <i>Electronic Communications in Probability</i>, vol. 28. Institute of Mathematical Statistics, pp. 1–12, 2023.","ista":"Dello Schiavo L, Lytvynov E. 2023. A Mecke-type characterization of the Dirichlet–Ferguson measure. Electronic Communications in Probability. 28, 1–12.","mla":"Dello Schiavo, Lorenzo, and Eugene Lytvynov. “A Mecke-Type Characterization of the Dirichlet–Ferguson Measure.” <i>Electronic Communications in Probability</i>, vol. 28, Institute of Mathematical Statistics, 2023, pp. 1–12, doi:<a href=\"https://doi.org/10.1214/23-ECP528\">10.1214/23-ECP528</a>.","chicago":"Dello Schiavo, Lorenzo, and Eugene Lytvynov. “A Mecke-Type Characterization of the Dirichlet–Ferguson Measure.” <i>Electronic Communications in Probability</i>. Institute of Mathematical Statistics, 2023. <a href=\"https://doi.org/10.1214/23-ECP528\">https://doi.org/10.1214/23-ECP528</a>.","apa":"Dello Schiavo, L., &#38; Lytvynov, E. (2023). A Mecke-type characterization of the Dirichlet–Ferguson measure. <i>Electronic Communications in Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/23-ECP528\">https://doi.org/10.1214/23-ECP528</a>"},"date_created":"2023-06-18T22:00:48Z","doi":"10.1214/23-ECP528","article_type":"original","_id":"13145","file_date_updated":"2023-06-19T09:37:40Z"},{"arxiv":1,"author":[{"last_name":"Hua","full_name":"Hua, Bobo","first_name":"Bobo"},{"last_name":"Keller","first_name":"Matthias","full_name":"Keller, Matthias"},{"full_name":"Schwarz, Michael","first_name":"Michael","last_name":"Schwarz"},{"orcid":"0000-0002-0519-4241","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","last_name":"Wirth","full_name":"Wirth, Melchior","first_name":"Melchior"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","main_file_link":[{"open_access":"1","url":" https://doi.org/10.48550/arXiv.1804.08353"}],"day":"01","oa_version":"Preprint","publication_identifier":{"issn":["0002-9939"],"eissn":["1088-6826"]},"month":"08","type":"journal_article","status":"public","title":"Sobolev-type inequalities and eigenvalue growth on graphs with finite measure","issue":"8","article_processing_charge":"No","oa":1,"date_updated":"2023-11-14T13:07:09Z","scopus_import":"1","intvolume":"       151","isi":1,"language":[{"iso":"eng"}],"publication":"Proceedings of the American Mathematical Society","publication_status":"published","abstract":[{"text":"In this note we study the eigenvalue growth of infinite graphs with discrete spectrum. We assume that the corresponding Dirichlet forms satisfy certain Sobolev-type inequalities and that the total measure is finite. In this sense, the associated operators on these graphs display similarities to elliptic operators on bounded domains in the continuum. Specifically, we prove lower bounds on the eigenvalue growth and show by examples that corresponding upper bounds cannot be established.","lang":"eng"}],"external_id":{"isi":["000988204400001"],"arxiv":["1804.08353"]},"volume":151,"quality_controlled":"1","department":[{"_id":"JaMa"}],"page":"3401-3414","date_published":"2023-08-01T00:00:00Z","publisher":"American Mathematical Society","date_created":"2023-07-02T22:00:43Z","citation":{"mla":"Hua, Bobo, et al. “Sobolev-Type Inequalities and Eigenvalue Growth on Graphs with Finite Measure.” <i>Proceedings of the American Mathematical Society</i>, vol. 151, no. 8, American Mathematical Society, 2023, pp. 3401–14, doi:<a href=\"https://doi.org/10.1090/proc/14361\">10.1090/proc/14361</a>.","chicago":"Hua, Bobo, Matthias Keller, Michael Schwarz, and Melchior Wirth. “Sobolev-Type Inequalities and Eigenvalue Growth on Graphs with Finite Measure.” <i>Proceedings of the American Mathematical Society</i>. American Mathematical Society, 2023. <a href=\"https://doi.org/10.1090/proc/14361\">https://doi.org/10.1090/proc/14361</a>.","ista":"Hua B, Keller M, Schwarz M, Wirth M. 2023. Sobolev-type inequalities and eigenvalue growth on graphs with finite measure. Proceedings of the American Mathematical Society. 151(8), 3401–3414.","short":"B. Hua, M. Keller, M. Schwarz, M. Wirth, Proceedings of the American Mathematical Society 151 (2023) 3401–3414.","ama":"Hua B, Keller M, Schwarz M, Wirth M. Sobolev-type inequalities and eigenvalue growth on graphs with finite measure. <i>Proceedings of the American Mathematical Society</i>. 2023;151(8):3401-3414. doi:<a href=\"https://doi.org/10.1090/proc/14361\">10.1090/proc/14361</a>","ieee":"B. Hua, M. Keller, M. Schwarz, and M. Wirth, “Sobolev-type inequalities and eigenvalue growth on graphs with finite measure,” <i>Proceedings of the American Mathematical Society</i>, vol. 151, no. 8. American Mathematical Society, pp. 3401–3414, 2023.","apa":"Hua, B., Keller, M., Schwarz, M., &#38; Wirth, M. (2023). Sobolev-type inequalities and eigenvalue growth on graphs with finite measure. <i>Proceedings of the American Mathematical Society</i>. American Mathematical Society. <a href=\"https://doi.org/10.1090/proc/14361\">https://doi.org/10.1090/proc/14361</a>"},"year":"2023","acknowledgement":"The second author was supported by the priority program SPP2026 of the German Research Foundation (DFG). The fourth author was supported by the German Academic Scholarship Foundation (Studienstiftung des deutschen Volkes) and by the German Research Foundation (DFG) via RTG 1523/2.","_id":"13177","article_type":"original","doi":"10.1090/proc/14361"},{"acknowledgement":"I am grateful to Boguslaw Zegarliński for asking me the questions in [3] and for helpful communication. I also want to thank Paata Ivanisvili for drawing [25] to my attention and for useful correspondence. Many thanks to the anonymous referee for the valuable comments and for pointing out some errors in an earlier version of the paper. This work is partially 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.","year":"2023","date_created":"2023-07-23T22:01:15Z","citation":{"ista":"Zhang H. 2023. Some convexity and monotonicity results of trace functionals. Annales Henri Poincare.","mla":"Zhang, Haonan. “Some Convexity and Monotonicity Results of Trace Functionals.” <i>Annales Henri Poincare</i>, Springer Nature, 2023, doi:<a href=\"https://doi.org/10.1007/s00023-023-01345-7\">10.1007/s00023-023-01345-7</a>.","chicago":"Zhang, Haonan. “Some Convexity and Monotonicity Results of Trace Functionals.” <i>Annales Henri Poincare</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00023-023-01345-7\">https://doi.org/10.1007/s00023-023-01345-7</a>.","ama":"Zhang H. Some convexity and monotonicity results of trace functionals. <i>Annales Henri Poincare</i>. 2023. doi:<a href=\"https://doi.org/10.1007/s00023-023-01345-7\">10.1007/s00023-023-01345-7</a>","ieee":"H. Zhang, “Some convexity and monotonicity results of trace functionals,” <i>Annales Henri Poincare</i>. Springer Nature, 2023.","short":"H. Zhang, Annales Henri Poincare (2023).","apa":"Zhang, H. (2023). Some convexity and monotonicity results of trace functionals. <i>Annales Henri Poincare</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00023-023-01345-7\">https://doi.org/10.1007/s00023-023-01345-7</a>"},"ec_funded":1,"_id":"13271","article_type":"original","doi":"10.1007/s00023-023-01345-7","publication_status":"epub_ahead","external_id":{"isi":["001025709100001"],"arxiv":["2108.05785"]},"abstract":[{"text":"In this paper, we prove the convexity of trace functionals (A,B,C)↦Tr|BpACq|s,\r\nfor parameters (p, q, s) that are best possible, where B and C are any n-by-n positive-definite matrices, and A is any n-by-n matrix. We also obtain the monotonicity versions of trace functionals of this type. As applications, we extend some results in Carlen et al. (Linear Algebra Appl 490:174–185, 2016), Hiai and Petz (Publ Res Inst Math Sci 48(3):525-542, 2012) and resolve a conjecture in Al-Rashed and Zegarliński (Infin Dimens Anal Quantum Probab Relat Top 17(4):1450029, 2014) in the matrix setting. Other conjectures in Al-Rashed and Zegarliński (Infin Dimens Anal Quantum Probab Relat Top 17(4):1450029, 2014) will also be discussed. We also show that some related trace functionals are not concave in general. Such concavity results were expected to hold in different problems.","lang":"eng"}],"project":[{"grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships"},{"name":"Curvature-dimension in noncommutative analysis","grant_number":"M03337","_id":"eb958bca-77a9-11ec-83b8-c565cb50d8d6"}],"publisher":"Springer Nature","date_published":"2023-07-08T00:00:00Z","department":[{"_id":"JaMa"}],"quality_controlled":"1","date_updated":"2023-12-13T11:33:46Z","oa":1,"article_processing_charge":"No","title":"Some convexity and monotonicity results of trace functionals","isi":1,"scopus_import":"1","language":[{"iso":"eng"}],"publication":"Annales Henri Poincare","author":[{"full_name":"Zhang, Haonan","first_name":"Haonan","id":"D8F41E38-9E66-11E9-A9E2-65C2E5697425","last_name":"Zhang"}],"arxiv":1,"publication_identifier":{"issn":["1424-0637"]},"month":"07","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2108.05785"}],"day":"08","oa_version":"Preprint","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","type":"journal_article","status":"public"},{"publication_status":"epub_ahead","external_id":{"arxiv":["2210.14468"],"isi":["001035665500001"]},"abstract":[{"lang":"eng","text":"Bohnenblust–Hille inequalities for Boolean cubes have been proven with dimension-free constants that grow subexponentially in the degree (Defant et al. in Math Ann 374(1):653–680, 2019). Such inequalities have found great applications in learning low-degree Boolean functions (Eskenazis and Ivanisvili in Proceedings of the 54th annual ACM SIGACT symposium on theory of computing, pp 203–207, 2022). Motivated by learning quantum observables, a qubit analogue of Bohnenblust–Hille inequality for Boolean cubes was recently conjectured in Rouzé et al. (Quantum Talagrand, KKL and Friedgut’s theorems and the learnability of quantum Boolean functions, 2022. arXiv preprint arXiv:2209.07279). The conjecture was resolved in Huang et al. (Learning to predict arbitrary quantum processes, 2022. arXiv preprint arXiv:2210.14894). In this paper, we give a new proof of these Bohnenblust–Hille inequalities for qubit system with constants that are dimension-free and of exponential growth in the degree. As a consequence, we obtain a junta theorem for low-degree polynomials. Using similar ideas, we also study learning problems of low degree quantum observables and Bohr’s radius phenomenon on quantum Boolean cubes."}],"project":[{"grant_number":"M03337","_id":"eb958bca-77a9-11ec-83b8-c565cb50d8d6","name":"Curvature-dimension in noncommutative analysis"}],"department":[{"_id":"JaMa"}],"quality_controlled":"1","publisher":"Springer Nature","date_published":"2023-07-24T00:00:00Z","citation":{"ista":"Volberg A, Zhang H. 2023. Noncommutative Bohnenblust–Hille inequalities. Mathematische Annalen.","chicago":"Volberg, Alexander, and Haonan Zhang. “Noncommutative Bohnenblust–Hille Inequalities.” <i>Mathematische Annalen</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00208-023-02680-0\">https://doi.org/10.1007/s00208-023-02680-0</a>.","mla":"Volberg, Alexander, and Haonan Zhang. “Noncommutative Bohnenblust–Hille Inequalities.” <i>Mathematische Annalen</i>, Springer Nature, 2023, doi:<a href=\"https://doi.org/10.1007/s00208-023-02680-0\">10.1007/s00208-023-02680-0</a>.","ieee":"A. Volberg and H. Zhang, “Noncommutative Bohnenblust–Hille inequalities,” <i>Mathematische Annalen</i>. Springer Nature, 2023.","ama":"Volberg A, Zhang H. Noncommutative Bohnenblust–Hille inequalities. <i>Mathematische Annalen</i>. 2023. doi:<a href=\"https://doi.org/10.1007/s00208-023-02680-0\">10.1007/s00208-023-02680-0</a>","short":"A. Volberg, H. Zhang, Mathematische Annalen (2023).","apa":"Volberg, A., &#38; Zhang, H. (2023). Noncommutative Bohnenblust–Hille inequalities. <i>Mathematische Annalen</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00208-023-02680-0\">https://doi.org/10.1007/s00208-023-02680-0</a>"},"date_created":"2023-07-30T22:01:03Z","acknowledgement":"The research of A.V. is supported by NSF DMS-1900286, DMS-2154402 and by Hausdorff Center for Mathematics. H.Z. is supported by the Lise Meitner fellowship, Austrian Science Fund (FWF) M3337. This work is partially supported by NSF DMS-1929284 while both authors were in residence at the Institute for Computational and Experimental Research in Mathematics in Providence, RI, during the Harmonic Analysis and Convexity program.","year":"2023","_id":"13318","article_type":"original","doi":"10.1007/s00208-023-02680-0","author":[{"last_name":"Volberg","first_name":"Alexander","full_name":"Volberg, Alexander"},{"id":"D8F41E38-9E66-11E9-A9E2-65C2E5697425","last_name":"Zhang","full_name":"Zhang, Haonan","first_name":"Haonan"}],"arxiv":1,"main_file_link":[{"url":"https://doi.org/10.1007/s00208-023-02680-0","open_access":"1"}],"oa_version":"Published Version","day":"24","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"issn":["0025-5831"],"eissn":["1432-1807"]},"month":"07","type":"journal_article","status":"public","title":"Noncommutative Bohnenblust–Hille inequalities","oa":1,"date_updated":"2023-12-13T11:36:20Z","article_processing_charge":"No","scopus_import":"1","isi":1,"language":[{"iso":"eng"}],"publication":"Mathematische Annalen"},{"scopus_import":"1","has_accepted_license":"1","intvolume":"       403","isi":1,"title":"Derivations and KMS-symmetric quantum Markov semigroups","article_processing_charge":"Yes (via OA deal)","date_updated":"2024-01-30T12:16:32Z","oa":1,"publication":"Communications in Mathematical Physics","language":[{"iso":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file":[{"date_created":"2024-01-30T12:15:11Z","date_updated":"2024-01-30T12:15:11Z","success":1,"checksum":"cca204e81891270216a0c84eb8bcd398","file_id":"14905","file_name":"2023_CommMathPhysics_Vernooij.pdf","content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_size":481209,"creator":"dernst"}],"day":"01","oa_version":"Published Version","month":"10","publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"arxiv":1,"author":[{"full_name":"Vernooij, Matthijs","first_name":"Matthijs","last_name":"Vernooij"},{"first_name":"Melchior","full_name":"Wirth, Melchior","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","last_name":"Wirth","orcid":"0000-0002-0519-4241"}],"status":"public","type":"journal_article","citation":{"apa":"Vernooij, M., &#38; Wirth, M. (2023). Derivations and KMS-symmetric quantum Markov semigroups. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-023-04795-6\">https://doi.org/10.1007/s00220-023-04795-6</a>","short":"M. Vernooij, M. Wirth, Communications in Mathematical Physics 403 (2023) 381–416.","ama":"Vernooij M, Wirth M. Derivations and KMS-symmetric quantum Markov semigroups. <i>Communications in Mathematical Physics</i>. 2023;403:381-416. doi:<a href=\"https://doi.org/10.1007/s00220-023-04795-6\">10.1007/s00220-023-04795-6</a>","ieee":"M. Vernooij and M. Wirth, “Derivations and KMS-symmetric quantum Markov semigroups,” <i>Communications in Mathematical Physics</i>, vol. 403. Springer Nature, pp. 381–416, 2023.","mla":"Vernooij, Matthijs, and Melchior Wirth. “Derivations and KMS-Symmetric Quantum Markov Semigroups.” <i>Communications in Mathematical Physics</i>, vol. 403, Springer Nature, 2023, pp. 381–416, doi:<a href=\"https://doi.org/10.1007/s00220-023-04795-6\">10.1007/s00220-023-04795-6</a>.","ista":"Vernooij M, Wirth M. 2023. Derivations and KMS-symmetric quantum Markov semigroups. Communications in Mathematical Physics. 403, 381–416.","chicago":"Vernooij, Matthijs, and Melchior Wirth. “Derivations and KMS-Symmetric Quantum Markov Semigroups.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00220-023-04795-6\">https://doi.org/10.1007/s00220-023-04795-6</a>."},"date_created":"2023-07-30T22:01:03Z","year":"2023","acknowledgement":"The authors are grateful to Martijn Caspers for helpful comments on a preliminary version of this manuscript. M. V. was supported by the NWO Vidi grant VI.Vidi.192.018 ‘Non-commutative harmonic analysis and rigidity of operator algebras’. M. W. was funded by the Austrian Science Fund (FWF) under the Esprit Programme [ESP 156]. For the purpose of Open Access, the authors have applied a CC BY public copyright licence to any Author Accepted Manuscript (AAM) version arising from this submission. Open access funding provided by Austrian Science Fund (FWF).","doi":"10.1007/s00220-023-04795-6","_id":"13319","article_type":"original","file_date_updated":"2024-01-30T12:15:11Z","abstract":[{"text":"We prove that the generator of the L2 implementation of a KMS-symmetric quantum Markov semigroup can be expressed as the square of a derivation with values in a Hilbert bimodule, extending earlier results by Cipriani and Sauvageot for tracially symmetric semigroups and the second-named author for GNS-symmetric semigroups. This result hinges on the introduction of a new completely positive map on the algebra of bounded operators on the GNS Hilbert space. This transformation maps symmetric Markov operators to symmetric Markov operators and is essential to obtain the required inner product on the Hilbert bimodule.","lang":"eng"}],"external_id":{"arxiv":["2303.15949"],"isi":["001033655400002"]},"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"ddc":["510"],"publication_status":"published","quality_controlled":"1","volume":403,"page":"381-416","department":[{"_id":"JaMa"}],"date_published":"2023-10-01T00:00:00Z","publisher":"Springer Nature","project":[{"_id":"34c6ea2d-11ca-11ed-8bc3-c04f3c502833","grant_number":"ESP156_N","name":"Gradient flow techniques for quantum Markov semigroups"}]},{"date_published":"2023-12-04T00:00:00Z","type":"preprint","status":"public","department":[{"_id":"NiBa"},{"_id":"JaMa"}],"project":[{"grant_number":"P32896","_id":"c08d3278-5a5b-11eb-8a69-fdb09b55f4b8","name":"Causes and consequences of population fragmentation"},{"name":"The impact of deleterious mutations on small populations","_id":"34d33d68-11ca-11ed-8bc3-ec13763c0ca8","grant_number":"26293"},{"_id":"34c872fe-11ca-11ed-8bc3-8534b82131e6","grant_number":"26380","name":"Polygenic Adaptation in a Metapopulation"}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","image":"/images/cc_by_nc_nd.png","short":"CC BY-NC-ND (4.0)","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)"},"month":"12","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","abstract":[{"lang":"eng","text":"Fragmented landscapes pose a significant threat to the persistence of species as they are highly susceptible to heightened risk of extinction due to the combined effects of genetic and demographic factors such as genetic drift and demographic stochasticity. This paper explores the intricate interplay between genetic load and extinction risk within metapopulations with a focus on understanding the impact of eco-evolutionary feedback mechanisms. We distinguish between two models of selection: soft selection, characterised by subpopulations maintaining carrying capacity despite load, and hard selection, where load can significantly affect population size. Within the soft selection framework, we investigate the impact of gene flow on genetic load at a single locus, while also considering the effect of selection strength and dominance coefficient. We subsequently build on this to examine how gene flow influences both population size and load under hard selection as well as identify critical thresholds for metapopulation persistence. Our analysis employs the diffusion, semi-deterministic and effective migration approximations. Our findings reveal that under soft selection, even modest levels of migration can significantly alleviate the burden of load. In sharp contrast, with hard selection, a much higher degree of gene flow is required to mitigate load and prevent the collapse of the metapopulation. Overall, this study sheds light into the crucial role migration plays in shaping the dynamics of genetic load and extinction risk in fragmented landscapes, offering valuable insights for conservation strategies and the preservation of diversity in a changing world."}],"oa_version":"Preprint","day":"04","main_file_link":[{"open_access":"1","url":"https://www.biorxiv.org/content/10.1101/2023.12.02.569702v1"}],"author":[{"id":"41AD96DC-F248-11E8-B48F-1D18A9856A87","last_name":"Olusanya","orcid":"0000-0003-1971-8314","first_name":"Oluwafunmilola O","full_name":"Olusanya, Oluwafunmilola O"},{"orcid":"0000-0002-6246-1465","id":"4E6DC800-AE37-11E9-AC72-31CAE5697425","last_name":"Khudiakova","full_name":"Khudiakova, Kseniia","first_name":"Kseniia"},{"id":"42377A0A-F248-11E8-B48F-1D18A9856A87","last_name":"Sachdeva","first_name":"Himani","full_name":"Sachdeva, Himani"}],"publication_status":"submitted","publication":"bioRxiv","doi":"10.1101/2023.12.02.569702","language":[{"iso":"eng"}],"_id":"14732","related_material":{"record":[{"status":"public","id":"14711","relation":"dissertation_contains"}]},"article_processing_charge":"No","year":"2023","oa":1,"date_updated":"2025-05-26T09:05:10Z","date_created":"2024-01-04T09:35:54Z","title":"Genetic load, eco-evolutionary feedback and extinction in a metapopulation","citation":{"short":"O.O. Olusanya, K. Khudiakova, H. Sachdeva, BioRxiv (n.d.).","ama":"Olusanya OO, Khudiakova K, Sachdeva H. Genetic load, eco-evolutionary feedback and extinction in a metapopulation. <i>bioRxiv</i>. doi:<a href=\"https://doi.org/10.1101/2023.12.02.569702\">10.1101/2023.12.02.569702</a>","ieee":"O. O. Olusanya, K. Khudiakova, and H. Sachdeva, “Genetic load, eco-evolutionary feedback and extinction in a metapopulation,” <i>bioRxiv</i>. .","chicago":"Olusanya, Oluwafunmilola O, Kseniia Khudiakova, and Himani Sachdeva. “Genetic Load, Eco-Evolutionary Feedback and Extinction in a Metapopulation.” <i>BioRxiv</i>, n.d. <a href=\"https://doi.org/10.1101/2023.12.02.569702\">https://doi.org/10.1101/2023.12.02.569702</a>.","mla":"Olusanya, Oluwafunmilola O., et al. “Genetic Load, Eco-Evolutionary Feedback and Extinction in a Metapopulation.” <i>BioRxiv</i>, doi:<a href=\"https://doi.org/10.1101/2023.12.02.569702\">10.1101/2023.12.02.569702</a>.","ista":"Olusanya OO, Khudiakova K, Sachdeva H. Genetic load, eco-evolutionary feedback and extinction in a metapopulation. bioRxiv, <a href=\"https://doi.org/10.1101/2023.12.02.569702\">10.1101/2023.12.02.569702</a>.","apa":"Olusanya, O. O., Khudiakova, K., &#38; Sachdeva, H. (n.d.). Genetic load, eco-evolutionary feedback and extinction in a metapopulation. <i>bioRxiv</i>. <a href=\"https://doi.org/10.1101/2023.12.02.569702\">https://doi.org/10.1101/2023.12.02.569702</a>"}},{"status":"public","type":"journal_article","arxiv":1,"author":[{"orcid":"0000-0002-9881-6870","last_name":"Dello Schiavo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","full_name":"Dello Schiavo, Lorenzo","first_name":"Lorenzo"}],"month":"03","publication_identifier":{"issn":["0926-2601"],"eissn":["1572-929X"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file":[{"creator":"dernst","access_level":"open_access","file_size":806391,"content_type":"application/pdf","relation":"main_file","success":1,"checksum":"625526482be300ca7281c91c30d41725","file_id":"14387","file_name":"2023_PotentialAnalysis_DelloSchiavo.pdf","date_created":"2023-10-04T09:18:59Z","date_updated":"2023-10-04T09:18:59Z"}],"day":"01","oa_version":"Published Version","language":[{"iso":"eng"}],"publication":"Potential Analysis","article_processing_charge":"Yes (via OA deal)","oa":1,"date_updated":"2023-10-04T09:19:12Z","title":"Ergodic decomposition of Dirichlet forms via direct integrals and applications","isi":1,"intvolume":"        58","has_accepted_license":"1","scopus_import":"1","project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"},{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems"},{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020"}],"date_published":"2023-03-01T00:00:00Z","publisher":"Springer Nature","volume":58,"quality_controlled":"1","department":[{"_id":"JaMa"}],"page":"573-615","publication_status":"published","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"ddc":["510"],"abstract":[{"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.","lang":"eng"}],"external_id":{"isi":["000704213400001"],"arxiv":["2003.01366"]},"_id":"10145","article_type":"original","file_date_updated":"2023-10-04T09:18:59Z","doi":"10.1007/s11118-021-09951-y","year":"2023","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.","date_created":"2021-10-17T22:01:17Z","citation":{"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.","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>","short":"L. Dello Schiavo, Potential Analysis 58 (2023) 573–615.","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>.","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>.","ista":"Dello Schiavo L. 2023. Ergodic decomposition of Dirichlet forms via direct integrals and applications. Potential Analysis. 58, 573–615.","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>"},"ec_funded":1},{"project":[{"grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships"},{"name":"Curvature-dimension in noncommutative analysis","grant_number":"M03337","_id":"eb958bca-77a9-11ec-83b8-c565cb50d8d6"},{"call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117"},{"name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"}],"date_published":"2023-03-01T00:00:00Z","publisher":"Springer Nature","quality_controlled":"1","volume":24,"department":[{"_id":"JaMa"}],"page":"717-750","publication_status":"published","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"ddc":["510"],"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."}],"external_id":{"isi":["000837499800002"],"arxiv":["2105.08303"]},"_id":"12087","article_type":"original","file_date_updated":"2023-08-14T11:38:28Z","doi":"10.1007/s00023-022-01220-x","year":"2023","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).","citation":{"ista":"Wirth M, Zhang H. 2023. Curvature-dimension conditions for symmetric quantum Markov semigroups. Annales Henri Poincare. 24, 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>.","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>.","short":"M. Wirth, H. Zhang, Annales Henri Poincare 24 (2023) 717–750.","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.","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>","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>"},"date_created":"2022-09-11T22:01:57Z","ec_funded":1,"type":"journal_article","status":"public","arxiv":1,"author":[{"orcid":"0000-0002-0519-4241","last_name":"Wirth","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","full_name":"Wirth, Melchior","first_name":"Melchior"},{"first_name":"Haonan","full_name":"Zhang, Haonan","last_name":"Zhang","id":"D8F41E38-9E66-11E9-A9E2-65C2E5697425"}],"month":"03","publication_identifier":{"issn":["1424-0637"]},"file":[{"relation":"main_file","access_level":"open_access","content_type":"application/pdf","file_size":554871,"creator":"dernst","date_updated":"2023-08-14T11:38:28Z","date_created":"2023-08-14T11:38:28Z","file_name":"2023_AnnalesHenriPoincare_Wirth.pdf","checksum":"8c7b185eba5ccd92ef55c120f654222c","file_id":"14051","success":1}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"01","oa_version":"Published Version","language":[{"iso":"eng"}],"publication":"Annales Henri Poincare","article_processing_charge":"Yes (via OA deal)","oa":1,"date_updated":"2023-08-14T11:39:28Z","title":"Curvature-dimension conditions for symmetric quantum Markov semigroups","isi":1,"has_accepted_license":"1","intvolume":"        24","scopus_import":"1"},{"doi":"10.1007/s00028-022-00859-7","file_date_updated":"2023-01-20T10:45:06Z","article_type":"original","_id":"12104","ec_funded":1,"article_number":"9","citation":{"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.","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).","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>.","ista":"Dello Schiavo L, Wirth M. 2023. Ergodic decompositions of Dirichlet forms under order isomorphisms. Journal of Evolution Equations. 23(1), 9.","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>."},"date_created":"2023-01-08T23:00:53Z","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).","year":"2023","department":[{"_id":"JaMa"}],"volume":23,"quality_controlled":"1","publisher":"Springer Nature","date_published":"2023-01-01T00:00:00Z","project":[{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems"},{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117","call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics"},{"_id":"34dbf174-11ca-11ed-8bc3-afe9d43d4b9c","grant_number":"E208","name":"Configuration Spaces over Non-Smooth Spaces"},{"_id":"34c6ea2d-11ca-11ed-8bc3-c04f3c502833","grant_number":"ESP156_N","name":"Gradient flow techniques for quantum Markov semigroups"}],"external_id":{"isi":["000906214600004"]},"abstract":[{"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.","lang":"eng"}],"ddc":["510"],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"publication_status":"published","publication":"Journal of Evolution Equations","language":[{"iso":"eng"}],"has_accepted_license":"1","intvolume":"        23","scopus_import":"1","isi":1,"title":"Ergodic decompositions of Dirichlet forms under order isomorphisms","date_updated":"2023-06-28T11:54:35Z","oa":1,"article_processing_charge":"Yes (via OA deal)","issue":"1","type":"journal_article","status":"public","day":"01","oa_version":"Published Version","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file":[{"creator":"dernst","relation":"main_file","access_level":"open_access","file_size":422612,"content_type":"application/pdf","checksum":"1f34f3e2cb521033de6154f274ea3a4e","file_id":"12325","file_name":"2023_JourEvolutionEquations_DelloSchiavo.pdf","success":1,"date_updated":"2023-01-20T10:45:06Z","date_created":"2023-01-20T10:45:06Z"}],"month":"01","publication_identifier":{"issn":["1424-3199"],"eissn":["1424-3202"]},"author":[{"full_name":"Dello Schiavo, Lorenzo","first_name":"Lorenzo","orcid":"0000-0002-9881-6870","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","last_name":"Dello Schiavo"},{"last_name":"Wirth","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","orcid":"0000-0002-0519-4241","full_name":"Wirth, Melchior","first_name":"Melchior"}]},{"ec_funded":1,"date_created":"2023-01-12T12:12:17Z","citation":{"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>","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>","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.","short":"T. Cremaschi, L. Dello Schiavo, Proceedings of the American Mathematical Society, Series B 9 (2022) 445–459.","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>.","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>.","ista":"Cremaschi T, Dello Schiavo L. 2022. Effective contraction of Skinning maps. Proceedings of the American Mathematical Society, Series B. 9(43), 445–459."},"year":"2022","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.","doi":"10.1090/bproc/134","article_type":"original","_id":"12177","file_date_updated":"2023-01-26T13:02:07Z","abstract":[{"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.","lang":"eng"}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","image":"/images/cc_by_nc_nd.png","short":"CC BY-NC-ND (4.0)","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)"},"ddc":["510"],"publication_status":"published","volume":9,"quality_controlled":"1","page":"445-459","department":[{"_id":"JaMa"}],"date_published":"2022-11-02T00:00:00Z","publisher":"American Mathematical Society","project":[{"grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems"},{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020"}],"has_accepted_license":"1","intvolume":"         9","scopus_import":"1","title":"Effective contraction of Skinning maps","article_processing_charge":"No","issue":"43","oa":1,"date_updated":"2023-01-26T13:04:13Z","publication":"Proceedings of the American Mathematical Society, Series B","language":[{"iso":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file":[{"relation":"main_file","file_size":326471,"access_level":"open_access","content_type":"application/pdf","creator":"dernst","date_updated":"2023-01-26T13:02:07Z","date_created":"2023-01-26T13:02:07Z","file_id":"12404","file_name":"2022_ProceedingsAMS_Cremaschi.pdf","checksum":"cb4a79937c1f60d4c329a10ee797f0d2","success":1}],"oa_version":"Published Version","day":"02","publication_identifier":{"issn":["2330-1511"]},"month":"11","author":[{"last_name":"Cremaschi","full_name":"Cremaschi, Tommaso","first_name":"Tommaso"},{"full_name":"Dello Schiavo, Lorenzo","first_name":"Lorenzo","orcid":"0000-0002-9881-6870","last_name":"Dello Schiavo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E"}],"type":"journal_article","status":"public"},{"acknowledgement":"Yu. K. thanks Professor Waldemar Hebisch for valuable discussions on the general context of multipliers on Lie groups. This work was started during an ICL-CNRS fellowship of the second\r\nnamed author at the Imperial College London. Yu. K. is supported by the ANR-19-CE40-0002 grant of the French National Research Agency (ANR). 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. R. A. was supported by the EPSRC grant EP/R003025. M. R. is supported by the EPSRC grant EP/R003025/2 and by the FWO Odysseus 1 grant G.0H94.18N: Analysis and Partial Differential Equations.","year":"2022","date_created":"2023-01-16T09:45:31Z","citation":{"short":"R. Akylzhanov, Y. Kuznetsova, M. Ruzhansky, H. Zhang, Mathematische Zeitschrift 302 (2022) 2327–2352.","ieee":"R. Akylzhanov, Y. Kuznetsova, M. Ruzhansky, and H. Zhang, “Norms of certain functions of a distinguished Laplacian on the ax + b groups,” <i>Mathematische Zeitschrift</i>, vol. 302, no. 4. Springer Nature, pp. 2327–2352, 2022.","ama":"Akylzhanov R, Kuznetsova Y, Ruzhansky M, Zhang H. Norms of certain functions of a distinguished Laplacian on the ax + b groups. <i>Mathematische Zeitschrift</i>. 2022;302(4):2327-2352. doi:<a href=\"https://doi.org/10.1007/s00209-022-03143-z\">10.1007/s00209-022-03143-z</a>","ista":"Akylzhanov R, Kuznetsova Y, Ruzhansky M, Zhang H. 2022. Norms of certain functions of a distinguished Laplacian on the ax + b groups. Mathematische Zeitschrift. 302(4), 2327–2352.","mla":"Akylzhanov, Rauan, et al. “Norms of Certain Functions of a Distinguished Laplacian on the Ax + b Groups.” <i>Mathematische Zeitschrift</i>, vol. 302, no. 4, Springer Nature, 2022, pp. 2327–52, doi:<a href=\"https://doi.org/10.1007/s00209-022-03143-z\">10.1007/s00209-022-03143-z</a>.","chicago":"Akylzhanov, Rauan, Yulia Kuznetsova, Michael Ruzhansky, and Haonan Zhang. “Norms of Certain Functions of a Distinguished Laplacian on the Ax + b Groups.” <i>Mathematische Zeitschrift</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s00209-022-03143-z\">https://doi.org/10.1007/s00209-022-03143-z</a>.","apa":"Akylzhanov, R., Kuznetsova, Y., Ruzhansky, M., &#38; Zhang, H. (2022). Norms of certain functions of a distinguished Laplacian on the ax + b groups. <i>Mathematische Zeitschrift</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00209-022-03143-z\">https://doi.org/10.1007/s00209-022-03143-z</a>"},"keyword":["General Mathematics"],"ec_funded":1,"_id":"12210","article_type":"original","doi":"10.1007/s00209-022-03143-z","publication_status":"published","external_id":{"isi":["000859680700001"],"arxiv":["2101.00584"]},"abstract":[{"lang":"eng","text":"The aim of this paper is to find new estimates for the norms of functions of a (minus) distinguished Laplace operator L on the ‘ax+b’ groups. The central part is devoted to spectrally localized wave propagators, that is, functions of the type ψ(L−−√)exp(itL−−√), with ψ∈C0(R). We show that for t→+∞, the convolution kernel kt of this operator satisfies\r\n∥kt∥1≍t,∥kt∥∞≍1,\r\nso that the upper estimates of D. Müller and C. Thiele (Studia Math., 2007) are sharp. As a necessary component, we recall the Plancherel density of L and spend certain time presenting and comparing different approaches to its calculation. Using its explicit form, we estimate uniform norms of several functions of the shifted Laplace-Beltrami operator Δ~, closely related to L. The functions include in particular exp(−tΔ~γ), t>0,γ>0, and (Δ~−z)s, with complex z, s."}],"project":[{"name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411"},{"name":"Curvature-dimension in noncommutative analysis","_id":"eb958bca-77a9-11ec-83b8-c565cb50d8d6","grant_number":"M03337"}],"publisher":"Springer Nature","date_published":"2022-12-01T00:00:00Z","department":[{"_id":"JaMa"}],"page":"2327-2352","quality_controlled":"1","volume":302,"date_updated":"2023-08-04T09:22:14Z","oa":1,"issue":"4","article_processing_charge":"No","title":"Norms of certain functions of a distinguished Laplacian on the ax + b groups","isi":1,"scopus_import":"1","intvolume":"       302","language":[{"iso":"eng"}],"publication":"Mathematische Zeitschrift","author":[{"full_name":"Akylzhanov, Rauan","first_name":"Rauan","last_name":"Akylzhanov"},{"first_name":"Yulia","full_name":"Kuznetsova, Yulia","last_name":"Kuznetsova"},{"full_name":"Ruzhansky, Michael","first_name":"Michael","last_name":"Ruzhansky"},{"last_name":"Zhang","id":"D8F41E38-9E66-11E9-A9E2-65C2E5697425","first_name":"Haonan","full_name":"Zhang, Haonan"}],"arxiv":1,"publication_identifier":{"issn":["0025-5874"],"eissn":["1432-1823"]},"month":"12","main_file_link":[{"url":"https://arxiv.org/abs/2101.00584","open_access":"1"}],"day":"01","oa_version":"Preprint","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","type":"journal_article","status":"public"},{"author":[{"last_name":"Carlen","full_name":"Carlen, Eric A.","first_name":"Eric A."},{"first_name":"Haonan","full_name":"Zhang, Haonan","id":"D8F41E38-9E66-11E9-A9E2-65C2E5697425","last_name":"Zhang"}],"oa_version":"Published Version","day":"01","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","file":[{"success":1,"file_name":"2022_LinearAlgebra_Carlen.pdf","file_id":"12415","checksum":"cf3cb7e7e34baa967849f01d8f0c1ae4","date_created":"2023-01-27T08:08:39Z","date_updated":"2023-01-27T08:08:39Z","creator":"dernst","file_size":441184,"content_type":"application/pdf","access_level":"open_access","relation":"main_file"}],"month":"12","publication_identifier":{"issn":["0024-3795"]},"status":"public","type":"journal_article","title":"Monotonicity versions of Epstein's concavity theorem and related inequalities","date_updated":"2023-08-04T09:24:51Z","oa":1,"article_processing_charge":"Yes (via OA deal)","intvolume":"       654","has_accepted_license":"1","scopus_import":"1","isi":1,"language":[{"iso":"eng"}],"publication":"Linear Algebra and its Applications","publication_status":"published","external_id":{"isi":["000860689600014"]},"abstract":[{"text":"Many trace inequalities can be expressed either as concavity/convexity theorems or as monotonicity theorems. A classic example is the joint convexity of the quantum relative entropy which is equivalent to the Data Processing Inequality. The latter says that quantum operations can never increase the relative entropy. The monotonicity versions often have many advantages, and often have direct physical application, as in the example just mentioned. Moreover, the monotonicity results are often valid for a larger class of maps than, say, quantum operations (which are completely positive). In this paper we prove several new monotonicity results, the first of which is a monotonicity theorem that has as a simple corollary a celebrated concavity theorem of Epstein. Our starting points are the monotonicity versions of the Lieb Concavity and the Lieb Convexity Theorems. We also give two new proofs of these in their general forms using interpolation. We then prove our new monotonicity theorems by several duality arguments.","lang":"eng"}],"ddc":["510"],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"project":[{"grant_number":"M03337","_id":"eb958bca-77a9-11ec-83b8-c565cb50d8d6","name":"Curvature-dimension in noncommutative analysis"}],"page":"289-310","department":[{"_id":"JaMa"}],"volume":654,"quality_controlled":"1","publisher":"Elsevier","date_published":"2022-12-01T00:00:00Z","citation":{"apa":"Carlen, E. A., &#38; Zhang, H. (2022). Monotonicity versions of Epstein’s concavity theorem and related inequalities. <i>Linear Algebra and Its Applications</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.laa.2022.09.001\">https://doi.org/10.1016/j.laa.2022.09.001</a>","ista":"Carlen EA, Zhang H. 2022. Monotonicity versions of Epstein’s concavity theorem and related inequalities. Linear Algebra and its Applications. 654, 289–310.","mla":"Carlen, Eric A., and Haonan Zhang. “Monotonicity Versions of Epstein’s Concavity Theorem and Related Inequalities.” <i>Linear Algebra and Its Applications</i>, vol. 654, Elsevier, 2022, pp. 289–310, doi:<a href=\"https://doi.org/10.1016/j.laa.2022.09.001\">10.1016/j.laa.2022.09.001</a>.","chicago":"Carlen, Eric A., and Haonan Zhang. “Monotonicity Versions of Epstein’s Concavity Theorem and Related Inequalities.” <i>Linear Algebra and Its Applications</i>. Elsevier, 2022. <a href=\"https://doi.org/10.1016/j.laa.2022.09.001\">https://doi.org/10.1016/j.laa.2022.09.001</a>.","ieee":"E. A. Carlen and H. Zhang, “Monotonicity versions of Epstein’s concavity theorem and related inequalities,” <i>Linear Algebra and its Applications</i>, vol. 654. Elsevier, pp. 289–310, 2022.","ama":"Carlen EA, Zhang H. Monotonicity versions of Epstein’s concavity theorem and related inequalities. <i>Linear Algebra and its Applications</i>. 2022;654:289-310. doi:<a href=\"https://doi.org/10.1016/j.laa.2022.09.001\">10.1016/j.laa.2022.09.001</a>","short":"E.A. Carlen, H. Zhang, Linear Algebra and Its Applications 654 (2022) 289–310."},"date_created":"2023-01-16T09:46:38Z","keyword":["Discrete Mathematics and Combinatorics","Geometry and Topology","Numerical Analysis","Algebra and Number Theory"],"acknowledgement":"Work partially supported by the Lise Meitner fellowship, Austrian Science Fund (FWF) M3337.","year":"2022","file_date_updated":"2023-01-27T08:08:39Z","_id":"12216","article_type":"original","doi":"10.1016/j.laa.2022.09.001"},{"_id":"12281","article_type":"original","doi":"10.3150/21-bej1390","keyword":["Statistics and Probability"],"citation":{"ista":"Franceschini C, Gonçalves P, Sau F. 2022. Symmetric inclusion process with slow boundary: Hydrodynamics and hydrostatics. Bernoulli. 28(2), 1340–1381.","mla":"Franceschini, Chiara, et al. “Symmetric Inclusion Process with Slow Boundary: Hydrodynamics and Hydrostatics.” <i>Bernoulli</i>, vol. 28, no. 2, Bernoulli Society for Mathematical Statistics and Probability, 2022, pp. 1340–81, doi:<a href=\"https://doi.org/10.3150/21-bej1390\">10.3150/21-bej1390</a>.","chicago":"Franceschini, Chiara, Patrícia Gonçalves, and Federico Sau. “Symmetric Inclusion Process with Slow Boundary: Hydrodynamics and Hydrostatics.” <i>Bernoulli</i>. Bernoulli Society for Mathematical Statistics and Probability, 2022. <a href=\"https://doi.org/10.3150/21-bej1390\">https://doi.org/10.3150/21-bej1390</a>.","short":"C. Franceschini, P. Gonçalves, F. Sau, Bernoulli 28 (2022) 1340–1381.","ama":"Franceschini C, Gonçalves P, Sau F. Symmetric inclusion process with slow boundary: Hydrodynamics and hydrostatics. <i>Bernoulli</i>. 2022;28(2):1340-1381. doi:<a href=\"https://doi.org/10.3150/21-bej1390\">10.3150/21-bej1390</a>","ieee":"C. Franceschini, P. Gonçalves, and F. Sau, “Symmetric inclusion process with slow boundary: Hydrodynamics and hydrostatics,” <i>Bernoulli</i>, vol. 28, no. 2. Bernoulli Society for Mathematical Statistics and Probability, pp. 1340–1381, 2022.","apa":"Franceschini, C., Gonçalves, P., &#38; Sau, F. (2022). Symmetric inclusion process with slow boundary: Hydrodynamics and hydrostatics. <i>Bernoulli</i>. Bernoulli Society for Mathematical Statistics and Probability. <a href=\"https://doi.org/10.3150/21-bej1390\">https://doi.org/10.3150/21-bej1390</a>"},"date_created":"2023-01-16T10:03:04Z","year":"2022","acknowledgement":"C.F. and P.G. thank FCT/Portugal for support through the project UID/MAT/04459/2013.\r\nThis project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovative programme (grant agreement No. 715734). F.S. was founded by the European Union’s Horizon 2020 research and innovation programme under the Marie-Skłodowska-Curie grant agreement No. 754411.\r\nF.S. wishes to thank Joe P. Chen for some fruitful discussions at an early stage of this work. F.S. thanks CAMGSD, IST, Lisbon, where part of this work has been done, and the European research and innovative programme No. 715734 for the kind hospitality.","ec_funded":1,"project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020"}],"volume":28,"quality_controlled":"1","page":"1340-1381","department":[{"_id":"JaMa"}],"date_published":"2022-05-01T00:00:00Z","publisher":"Bernoulli Society for Mathematical Statistics and Probability","publication_status":"published","abstract":[{"lang":"eng","text":"We study the hydrodynamic and hydrostatic limits of the one-dimensional open symmetric inclusion process with slow boundary. Depending on the value of the parameter tuning the interaction rate of the bulk of the system with the boundary, we obtain a linear heat equation with either Dirichlet, Robin or Neumann boundary conditions as hydrodynamic equation. In our approach, we combine duality and first-second class particle techniques to reduce the scaling limit of the inclusion process to the limiting behavior of a single, non-interacting, particle."}],"external_id":{"arxiv":["2007.11998"],"isi":["000766619100025"]},"language":[{"iso":"eng"}],"publication":"Bernoulli","title":"Symmetric inclusion process with slow boundary: Hydrodynamics and hydrostatics","article_processing_charge":"No","issue":"2","oa":1,"date_updated":"2023-08-04T10:27:35Z","intvolume":"        28","scopus_import":"1","isi":1,"status":"public","type":"journal_article","arxiv":1,"author":[{"last_name":"Franceschini","full_name":"Franceschini, Chiara","first_name":"Chiara"},{"full_name":"Gonçalves, Patrícia","first_name":"Patrícia","last_name":"Gonçalves"},{"last_name":"Sau","id":"E1836206-9F16-11E9-8814-AEFDE5697425","first_name":"Federico","full_name":"Sau, Federico"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","day":"01","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2007.11998","open_access":"1"}],"oa_version":"Preprint","publication_identifier":{"issn":["1350-7265"]},"month":"05"},{"project":[{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117","call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics"},{"name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"department":[{"_id":"JaMa"}],"page":"1815-1832","quality_controlled":"1","volume":384,"publisher":"Springer Nature","date_published":"2022-12-01T00:00:00Z","publication_status":"published","external_id":{"isi":["000734150200001"],"arxiv":["2110.05137"]},"abstract":[{"lang":"eng","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."}],"ddc":["510"],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"file_date_updated":"2022-01-03T11:08:31Z","article_type":"original","_id":"10588","doi":"10.1007/s00208-021-02331-2","date_created":"2022-01-02T23:01:35Z","citation":{"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>.","ista":"Dello Schiavo L, Suzuki K. 2022. Sobolev-to-Lipschitz property on QCD- spaces and applications. Mathematische Annalen. 384, 1815–1832.","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.","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>","short":"L. Dello Schiavo, K. Suzuki, Mathematische Annalen 384 (2022) 1815–1832.","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>"},"keyword":["quasi curvature-dimension condition","sub-riemannian geometry","Sobolev-to-Lipschitz property","Varadhan short-time asymptotics"],"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.","year":"2022","ec_funded":1,"status":"public","type":"journal_article","author":[{"first_name":"Lorenzo","full_name":"Dello Schiavo, Lorenzo","last_name":"Dello Schiavo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","orcid":"0000-0002-9881-6870"},{"last_name":"Suzuki","full_name":"Suzuki, Kohei","first_name":"Kohei"}],"arxiv":1,"day":"01","oa_version":"Published Version","file":[{"creator":"alisjak","content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_size":410090,"checksum":"2593abbf195e38efa93b6006b1e90eb1","file_id":"10596","file_name":"2021_MathAnn_DelloSchiavo.pdf","success":1,"date_updated":"2022-01-03T11:08:31Z","date_created":"2022-01-03T11:08:31Z"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","month":"12","publication_identifier":{"eissn":["1432-1807"],"issn":["0025-5831"]},"language":[{"iso":"eng"}],"publication":"Mathematische Annalen","title":"Sobolev-to-Lipschitz property on QCD- spaces and applications","oa":1,"date_updated":"2023-08-02T13:39:05Z","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","scopus_import":"1","intvolume":"       384","isi":1},{"publication_status":"published","abstract":[{"text":"We consider symmetric partial exclusion and inclusion processes in a general graph in contact with reservoirs, where we allow both for edge disorder and well-chosen site disorder. We extend the classical dualities to this context and then we derive new orthogonal polynomial dualities. From the classical dualities, we derive the uniqueness of the non-equilibrium steady state and obtain correlation inequalities. Starting from the orthogonal polynomial dualities, we show universal properties of n-point correlation functions in the non-equilibrium steady state for systems with at most two different reservoir parameters, such as a chain with reservoirs at left and right ends.","lang":"eng"},{"text":"Nous considérons des processus d’exclusion partielle, et des processus d’inclusion sur un graphe général en contact avec des réservoirs. Nous autorisons la présence de inhomogenéités sur les arrêts ainsi que sur les sommets du graph. Nous généralisons les “dualités classiques” dans ce contexte et nous démontrons des nouvelles dualités orthogonales. À partir des dualités classiques, nous démontrons l’unicité de l’état stationnaire non-équilibre, ainsi que des inégalités de corrélation. À partir des dualités orthogonales nous démontrons des propriétés universelles des fonctions de corrélation à n points dans l’état stationnaire non-équilibre pour des systèmes avec deux paramètres de réservoirs inégaux, comme par exemple une chaîne avec des réservoirs à droite et à gauche.","lang":"fre"}],"external_id":{"isi":["000752489300010"],"arxiv":["2007.08272"]},"project":[{"grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020"}],"volume":58,"quality_controlled":"1","page":"220-247","department":[{"_id":"JaMa"}],"date_published":"2022-02-01T00:00:00Z","publisher":"Institute of Mathematical Statistics","citation":{"apa":"Floreani, S., Redig, F., &#38; Sau, F. (2022). Orthogonal polynomial duality of boundary driven particle systems and non-equilibrium correlations. <i>Annales de l’institut Henri Poincare (B) Probability and Statistics</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/21-AIHP1163\">https://doi.org/10.1214/21-AIHP1163</a>","ama":"Floreani S, Redig F, Sau F. Orthogonal polynomial duality of boundary driven particle systems and non-equilibrium correlations. <i>Annales de l’institut Henri Poincare (B) Probability and Statistics</i>. 2022;58(1):220-247. doi:<a href=\"https://doi.org/10.1214/21-AIHP1163\">10.1214/21-AIHP1163</a>","ieee":"S. Floreani, F. Redig, and F. Sau, “Orthogonal polynomial duality of boundary driven particle systems and non-equilibrium correlations,” <i>Annales de l’institut Henri Poincare (B) Probability and Statistics</i>, vol. 58, no. 1. Institute of Mathematical Statistics, pp. 220–247, 2022.","short":"S. Floreani, F. Redig, F. Sau, Annales de l’institut Henri Poincare (B) Probability and Statistics 58 (2022) 220–247.","mla":"Floreani, Simone, et al. “Orthogonal Polynomial Duality of Boundary Driven Particle Systems and Non-Equilibrium Correlations.” <i>Annales de l’institut Henri Poincare (B) Probability and Statistics</i>, vol. 58, no. 1, Institute of Mathematical Statistics, 2022, pp. 220–47, doi:<a href=\"https://doi.org/10.1214/21-AIHP1163\">10.1214/21-AIHP1163</a>.","chicago":"Floreani, Simone, Frank Redig, and Federico Sau. “Orthogonal Polynomial Duality of Boundary Driven Particle Systems and Non-Equilibrium Correlations.” <i>Annales de l’institut Henri Poincare (B) Probability and Statistics</i>. Institute of Mathematical Statistics, 2022. <a href=\"https://doi.org/10.1214/21-AIHP1163\">https://doi.org/10.1214/21-AIHP1163</a>.","ista":"Floreani S, Redig F, Sau F. 2022. Orthogonal polynomial duality of boundary driven particle systems and non-equilibrium correlations. Annales de l’institut Henri Poincare (B) Probability and Statistics. 58(1), 220–247."},"date_created":"2022-02-27T23:01:50Z","year":"2022","acknowledgement":"The authors would like to thank Gioia Carinci and Cristian Giardinà for useful discussions. F.R. and S.F. thank Jean-René Chazottes for a stay at CPHT (Institut Polytechnique de Paris), in the realm of Chaire d’Alembert (Paris-Saclay University), where part of this work was performed. S.F. acknowledges Simona Villa for her support in creating the picture. S.F. acknowledges financial support from NWO via the grant TOP1.17.019. F.S. acknowledges financial support from the European Union’s Horizon 2020 research and innovation programme under the Marie-Skłodowska-Curie grant agreement No. 754411.","ec_funded":1,"article_type":"original","_id":"10797","doi":"10.1214/21-AIHP1163","arxiv":1,"author":[{"full_name":"Floreani, Simone","first_name":"Simone","last_name":"Floreani"},{"full_name":"Redig, Frank","first_name":"Frank","last_name":"Redig"},{"first_name":"Federico","full_name":"Sau, Federico","id":"E1836206-9F16-11E9-8814-AEFDE5697425","last_name":"Sau"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","main_file_link":[{"url":"https://arxiv.org/abs/2007.08272","open_access":"1"}],"day":"01","oa_version":"Preprint","publication_identifier":{"issn":["0246-0203"]},"month":"02","status":"public","type":"journal_article","title":"Orthogonal polynomial duality of boundary driven particle systems and non-equilibrium correlations","issue":"1","article_processing_charge":"No","oa":1,"date_updated":"2023-10-17T12:49:43Z","intvolume":"        58","scopus_import":"1","isi":1,"language":[{"iso":"eng"}],"publication":"Annales de l'institut Henri Poincare (B) Probability and Statistics"},{"project":[{"name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504"},{"name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117"}],"department":[{"_id":"JaMa"}],"volume":187,"quality_controlled":"1","publisher":"Springer Nature","date_published":"2022-04-08T00:00:00Z","publication_status":"published","external_id":{"isi":["000780305000001"]},"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."}],"ddc":["510","530"],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"file_date_updated":"2022-04-29T11:24:23Z","article_type":"original","_id":"11330","doi":"10.1007/s10955-022-02911-9","citation":{"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>.","ista":"Wirth M. 2022. A dual formula for the noncommutative transport distance. Journal of Statistical Physics. 187(2), 19.","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>","ieee":"M. Wirth, “A dual formula for the noncommutative transport distance,” <i>Journal of Statistical Physics</i>, vol. 187, no. 2. Springer Nature, 2022.","short":"M. Wirth, Journal of Statistical Physics 187 (2022)."},"date_created":"2022-04-24T22:01:43Z","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).","year":"2022","ec_funded":1,"article_number":"19","status":"public","type":"journal_article","author":[{"orcid":"0000-0002-0519-4241","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","last_name":"Wirth","full_name":"Wirth, Melchior","first_name":"Melchior"}],"day":"08","oa_version":"Published Version","file":[{"checksum":"f3e0b00884b7dde31347a3756788b473","file_id":"11338","file_name":"2022_JourStatisticalPhysics_Wirth.pdf","success":1,"date_updated":"2022-04-29T11:24:23Z","date_created":"2022-04-29T11:24:23Z","creator":"dernst","relation":"main_file","content_type":"application/pdf","access_level":"open_access","file_size":362119}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication_identifier":{"issn":["00224715"],"eissn":["15729613"]},"month":"04","language":[{"iso":"eng"}],"publication":"Journal of Statistical Physics","title":"A dual formula for the noncommutative transport distance","oa":1,"date_updated":"2023-08-03T06:37:49Z","issue":"2","article_processing_charge":"Yes (via OA deal)","intvolume":"       187","scopus_import":"1","has_accepted_license":"1","isi":1},{"scopus_import":"1","intvolume":"        50","isi":1,"title":"The Dirichlet–Ferguson diffusion on the space of probability measures over a closed Riemannian manifold","oa":1,"date_updated":"2023-10-17T12:50:24Z","issue":"2","article_processing_charge":"No","publication":"Annals of Probability","language":[{"iso":"eng"}],"main_file_link":[{"url":" https://doi.org/10.48550/arXiv.1811.11598","open_access":"1"}],"day":"01","oa_version":"Preprint","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","month":"03","publication_identifier":{"issn":["0091-1798"],"eissn":["2168-894X"]},"author":[{"last_name":"Dello Schiavo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","orcid":"0000-0002-9881-6870","first_name":"Lorenzo","full_name":"Dello Schiavo, Lorenzo"}],"arxiv":1,"status":"public","type":"journal_article","ec_funded":1,"citation":{"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>","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>.","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.","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>.","short":"L. Dello Schiavo, Annals of Probability 50 (2022) 591–648.","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.","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>"},"date_created":"2022-05-08T22:01:44Z","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).","year":"2022","doi":"10.1214/21-AOP1541","_id":"11354","article_type":"original","external_id":{"arxiv":["1811.11598"],"isi":["000773518500005"]},"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","department":[{"_id":"JaMa"}],"page":"591-648","volume":50,"quality_controlled":"1","publisher":"Institute of Mathematical Statistics","date_published":"2022-03-01T00:00:00Z","project":[{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117","call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics"},{"grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems"}]}]