[{"day":"02","type":"journal_article","intvolume":"         9","status":"public","publication":"Proceedings of the American Mathematical Society, Series B","issue":"43","file_date_updated":"2023-01-26T13:02:07Z","page":"445-459","month":"11","article_type":"original","date_published":"2022-11-02T00:00:00Z","scopus_import":"1","publisher":"American Mathematical Society","language":[{"iso":"eng"}],"has_accepted_license":"1","license":"https://creativecommons.org/licenses/by-nc-nd/4.0/","department":[{"_id":"JaMa"}],"file":[{"checksum":"cb4a79937c1f60d4c329a10ee797f0d2","date_created":"2023-01-26T13:02:07Z","file_size":326471,"file_name":"2022_ProceedingsAMS_Cremaschi.pdf","access_level":"open_access","date_updated":"2023-01-26T13:02:07Z","success":1,"file_id":"12404","creator":"dernst","relation":"main_file","content_type":"application/pdf"}],"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>","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.","chicago":"Cremaschi, Tommaso, and Lorenzo Dello Schiavo. “Effective Contraction of Skinning Maps.” <i>Proceedings of the American Mathematical Society, Series B</i>. American Mathematical Society, 2022. <a href=\"https://doi.org/10.1090/bproc/134\">https://doi.org/10.1090/bproc/134</a>.","ama":"Cremaschi T, Dello Schiavo L. Effective contraction of Skinning maps. <i>Proceedings of the American Mathematical Society, Series B</i>. 2022;9(43):445-459. doi:<a href=\"https://doi.org/10.1090/bproc/134\">10.1090/bproc/134</a>","mla":"Cremaschi, Tommaso, and Lorenzo Dello Schiavo. “Effective Contraction of Skinning Maps.” <i>Proceedings of the American Mathematical Society, Series B</i>, vol. 9, no. 43, American Mathematical Society, 2022, pp. 445–59, doi:<a href=\"https://doi.org/10.1090/bproc/134\">10.1090/bproc/134</a>.","short":"T. Cremaschi, L. Dello Schiavo, Proceedings of the American Mathematical Society, Series B 9 (2022) 445–459.","ista":"Cremaschi T, Dello Schiavo L. 2022. Effective contraction of Skinning maps. Proceedings of the American Mathematical Society, Series B. 9(43), 445–459."},"publication_status":"published","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"}],"author":[{"last_name":"Cremaschi","full_name":"Cremaschi, Tommaso","first_name":"Tommaso"},{"id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","first_name":"Lorenzo","orcid":"0000-0002-9881-6870","full_name":"Dello Schiavo, Lorenzo","last_name":"Dello Schiavo"}],"article_processing_charge":"No","oa":1,"volume":9,"date_updated":"2023-01-26T13:04:13Z","publication_identifier":{"issn":["2330-1511"]},"_id":"12177","oa_version":"Published Version","project":[{"grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"},{"grant_number":"716117","call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425","name":"Optimal Transport and Stochastic Dynamics"}],"quality_controlled":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","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.","year":"2022","doi":"10.1090/bproc/134","ec_funded":1,"title":"Effective contraction of Skinning maps","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","image":"/images/cc_by_nc_nd.png","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","short":"CC BY-NC-ND (4.0)"},"ddc":["510"]},{"date_published":"2022-12-01T00:00:00Z","article_type":"original","month":"12","language":[{"iso":"eng"}],"publisher":"Springer Nature","scopus_import":"1","department":[{"_id":"JaMa"}],"date_created":"2023-01-16T09:45:31Z","type":"journal_article","day":"01","status":"public","intvolume":"       302","page":"2327-2352","issue":"4","publication":"Mathematische Zeitschrift","ec_funded":1,"year":"2022","doi":"10.1007/s00209-022-03143-z","title":"Norms of certain functions of a distinguished Laplacian on the ax + b groups","external_id":{"arxiv":["2101.00584"],"isi":["000859680700001"]},"main_file_link":[{"url":"https://arxiv.org/abs/2101.00584","open_access":"1"}],"isi":1,"publication_status":"published","citation":{"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>","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>.","short":"R. Akylzhanov, Y. Kuznetsova, M. Ruzhansky, H. Zhang, Mathematische Zeitschrift 302 (2022) 2327–2352.","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.","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>","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.","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>."},"keyword":["General Mathematics"],"author":[{"full_name":"Akylzhanov, Rauan","last_name":"Akylzhanov","first_name":"Rauan"},{"first_name":"Yulia","last_name":"Kuznetsova","full_name":"Kuznetsova, Yulia"},{"first_name":"Michael","full_name":"Ruzhansky, Michael","last_name":"Ruzhansky"},{"id":"D8F41E38-9E66-11E9-A9E2-65C2E5697425","full_name":"Zhang, Haonan","last_name":"Zhang","first_name":"Haonan"}],"abstract":[{"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.","lang":"eng"}],"oa":1,"volume":302,"date_updated":"2023-08-04T09:22:14Z","article_processing_charge":"No","arxiv":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","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.","project":[{"call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"},{"_id":"eb958bca-77a9-11ec-83b8-c565cb50d8d6","name":"Curvature-dimension in noncommutative analysis","grant_number":"M03337"}],"quality_controlled":"1","oa_version":"Preprint","_id":"12210","publication_identifier":{"issn":["0025-5874"],"eissn":["1432-1823"]}},{"language":[{"iso":"eng"}],"publisher":"Elsevier","scopus_import":"1","date_published":"2022-12-01T00:00:00Z","article_type":"original","month":"12","file":[{"success":1,"creator":"dernst","file_id":"12415","relation":"main_file","content_type":"application/pdf","checksum":"cf3cb7e7e34baa967849f01d8f0c1ae4","date_created":"2023-01-27T08:08:39Z","file_size":441184,"file_name":"2022_LinearAlgebra_Carlen.pdf","access_level":"open_access","date_updated":"2023-01-27T08:08:39Z"}],"date_created":"2023-01-16T09:46:38Z","department":[{"_id":"JaMa"}],"has_accepted_license":"1","status":"public","intvolume":"       654","type":"journal_article","day":"01","page":"289-310","file_date_updated":"2023-01-27T08:08:39Z","publication":"Linear Algebra and its Applications","title":"Monotonicity versions of Epstein's concavity theorem and related inequalities","external_id":{"isi":["000860689600014"]},"doi":"10.1016/j.laa.2022.09.001","year":"2022","ddc":["510"],"isi":1,"tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"keyword":["Discrete Mathematics and Combinatorics","Geometry and Topology","Numerical Analysis","Algebra and Number Theory"],"author":[{"full_name":"Carlen, Eric A.","last_name":"Carlen","first_name":"Eric A."},{"last_name":"Zhang","full_name":"Zhang, Haonan","first_name":"Haonan","id":"D8F41E38-9E66-11E9-A9E2-65C2E5697425"}],"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"}],"publication_status":"published","citation":{"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>.","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>","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.","short":"E.A. Carlen, H. Zhang, Linear Algebra and Its Applications 654 (2022) 289–310.","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>.","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>"},"acknowledgement":"Work partially supported by the Lise Meitner fellowship, Austrian Science Fund (FWF) M3337.","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","project":[{"_id":"eb958bca-77a9-11ec-83b8-c565cb50d8d6","name":"Curvature-dimension in noncommutative analysis","grant_number":"M03337"}],"oa_version":"Published Version","quality_controlled":"1","_id":"12216","publication_identifier":{"issn":["0024-3795"]},"volume":654,"date_updated":"2023-08-04T09:24:51Z","oa":1,"article_processing_charge":"Yes (via OA deal)"},{"citation":{"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>.","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>","ista":"Franceschini C, Gonçalves P, Sau F. 2022. Symmetric inclusion process with slow boundary: Hydrodynamics and hydrostatics. Bernoulli. 28(2), 1340–1381.","short":"C. Franceschini, P. Gonçalves, F. Sau, Bernoulli 28 (2022) 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>.","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>"},"publication_status":"published","abstract":[{"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.","lang":"eng"}],"keyword":["Statistics and Probability"],"author":[{"first_name":"Chiara","last_name":"Franceschini","full_name":"Franceschini, Chiara"},{"first_name":"Patrícia","last_name":"Gonçalves","full_name":"Gonçalves, Patrícia"},{"id":"E1836206-9F16-11E9-8814-AEFDE5697425","last_name":"Sau","full_name":"Sau, Federico","first_name":"Federico"}],"arxiv":1,"article_processing_charge":"No","oa":1,"volume":28,"date_updated":"2023-08-04T10:27:35Z","publication_identifier":{"issn":["1350-7265"]},"_id":"12281","project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","grant_number":"754411"}],"quality_controlled":"1","oa_version":"Preprint","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.","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","doi":"10.3150/21-bej1390","year":"2022","ec_funded":1,"title":"Symmetric inclusion process with slow boundary: Hydrodynamics and hydrostatics","external_id":{"arxiv":["2007.11998"],"isi":["000766619100025"]},"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2007.11998","open_access":"1"}],"isi":1,"day":"01","type":"journal_article","intvolume":"        28","status":"public","publication":"Bernoulli","issue":"2","page":"1340-1381","month":"05","date_published":"2022-05-01T00:00:00Z","article_type":"original","scopus_import":"1","publisher":"Bernoulli Society for Mathematical Statistics and Probability","language":[{"iso":"eng"}],"department":[{"_id":"JaMa"}],"date_created":"2023-01-16T10:03:04Z"},{"doi":"10.1017/S0013091521000080","year":"2021","external_id":{"isi":["000721363700003"],"arxiv":["1912.03670"]},"title":"Self-adjoint extensions of bipartite Hamiltonians","isi":1,"main_file_link":[{"url":"https://doi.org/10.1017/S0013091521000080","open_access":"1"}],"publication_status":"published","citation":{"short":"D. Lenz, T. Weinmann, M. Wirth, Proceedings of the Edinburgh Mathematical Society 64 (2021) 443–447.","ista":"Lenz D, Weinmann T, Wirth M. 2021. Self-adjoint extensions of bipartite Hamiltonians. Proceedings of the Edinburgh Mathematical Society. 64(3), 443–447.","mla":"Lenz, Daniel, et al. “Self-Adjoint Extensions of Bipartite Hamiltonians.” <i>Proceedings of the Edinburgh Mathematical Society</i>, vol. 64, no. 3, Cambridge University Press, 2021, pp. 443–47, doi:<a href=\"https://doi.org/10.1017/S0013091521000080\">10.1017/S0013091521000080</a>.","ama":"Lenz D, Weinmann T, Wirth M. Self-adjoint extensions of bipartite Hamiltonians. <i>Proceedings of the Edinburgh Mathematical Society</i>. 2021;64(3):443-447. doi:<a href=\"https://doi.org/10.1017/S0013091521000080\">10.1017/S0013091521000080</a>","chicago":"Lenz, Daniel, Timon Weinmann, and Melchior Wirth. “Self-Adjoint Extensions of Bipartite Hamiltonians.” <i>Proceedings of the Edinburgh Mathematical Society</i>. Cambridge University Press, 2021. <a href=\"https://doi.org/10.1017/S0013091521000080\">https://doi.org/10.1017/S0013091521000080</a>.","apa":"Lenz, D., Weinmann, T., &#38; Wirth, M. (2021). Self-adjoint extensions of bipartite Hamiltonians. <i>Proceedings of the Edinburgh Mathematical Society</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/S0013091521000080\">https://doi.org/10.1017/S0013091521000080</a>","ieee":"D. Lenz, T. Weinmann, and M. Wirth, “Self-adjoint extensions of bipartite Hamiltonians,” <i>Proceedings of the Edinburgh Mathematical Society</i>, vol. 64, no. 3. Cambridge University Press, pp. 443–447, 2021."},"abstract":[{"text":"We compute the deficiency spaces of operators of the form 𝐻𝐴⊗̂ 𝐼+𝐼⊗̂ 𝐻𝐵, for symmetric 𝐻𝐴 and self-adjoint 𝐻𝐵. This enables us to construct self-adjoint extensions (if they exist) by means of von Neumann's theory. The structure of the deficiency spaces for this case was asserted already in Ibort et al. [Boundary dynamics driven entanglement, J. Phys. A: Math. Theor. 47(38) (2014) 385301], but only proven under the restriction of 𝐻𝐵 having discrete, non-degenerate spectrum.","lang":"eng"}],"author":[{"last_name":"Lenz","full_name":"Lenz, Daniel","first_name":"Daniel"},{"full_name":"Weinmann, Timon","last_name":"Weinmann","first_name":"Timon"},{"id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","first_name":"Melchior","last_name":"Wirth","full_name":"Wirth, Melchior","orcid":"0000-0002-0519-4241"}],"arxiv":1,"volume":64,"date_updated":"2023-08-17T07:12:05Z","oa":1,"article_processing_charge":"No","_id":"9627","publication_identifier":{"eissn":["1464-3839"],"issn":["0013-0915"]},"acknowledgement":"M. W. gratefully acknowledges financial support by the German Academic Scholarship Foundation (Studienstiftung des deutschen Volkes). T.W. thanks PAO Gazprom Neft, the Euler International Mathematical Institute in Saint Petersburg and ORISA GmbH for their financial support in the form of scholarships during his Master's and Bachelor's studies respectively. The authors want to thank Mark Malamud for pointing out the reference [1] to them. This work was supported by the Ministry of Science and Higher Education of the Russian Federation, agreement No 075-15-2019-1619.","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa_version":"Published Version","quality_controlled":"1","month":"08","date_published":"2021-08-01T00:00:00Z","article_type":"original","publisher":"Cambridge University Press","scopus_import":"1","language":[{"iso":"eng"}],"department":[{"_id":"JaMa"}],"date_created":"2021-07-04T22:01:24Z","day":"01","type":"journal_article","intvolume":"        64","status":"public","issue":"3","publication":"Proceedings of the Edinburgh Mathematical Society","page":"443-447"},{"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2005.14177"}],"external_id":{"arxiv":["2005.14177"]},"title":"Trajectorial dissipation and gradient flow for the relative entropy in Markov chains","ec_funded":1,"doi":"10.4310/CIS.2021.v21.n4.a1","year":"2021","project":[{"grant_number":"716117","call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425"},{"name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504"}],"quality_controlled":"1","oa_version":"Preprint","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","acknowledgement":"I.K. acknowledges support from the U.S. National Science Foundation under Grant NSF-DMS-20-04997. J.M. acknowledges support from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 716117) and from the Austrian Science Fund (FWF) through project F65. W.S. acknowledges support from the Austrian Science Fund (FWF) under grant P28861 and by the Vienna Science and Technology Fund (WWTF) through projects MA14-008 and MA16-021.","publication_identifier":{"issn":["1526-7555"]},"_id":"10023","article_processing_charge":"No","oa":1,"volume":21,"date_updated":"2021-09-20T12:51:18Z","arxiv":1,"author":[{"first_name":"Ioannis","full_name":"Karatzas, Ioannis","last_name":"Karatzas"},{"id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","last_name":"Maas","full_name":"Maas, Jan","orcid":"0000-0002-0845-1338","first_name":"Jan"},{"last_name":"Schachermayer","full_name":"Schachermayer, Walter","first_name":"Walter"}],"keyword":["Markov Chain","relative entropy","time reversal","steepest descent","gradient flow"],"abstract":[{"text":"We study the temporal dissipation of variance and relative entropy for ergodic Markov Chains in continuous time, and compute explicitly the corresponding dissipation rates. These are identified, as is well known, in the case of the variance in terms of an appropriate Hilbertian norm; and in the case of the relative entropy, in terms of a Dirichlet form which morphs into a version of the familiar Fisher information under conditions of detailed balance. Here we obtain trajectorial versions of these results, valid along almost every path of the random motion and most transparent in the backwards direction of time. Martingale arguments and time reversal play crucial roles, as in the recent work of Karatzas, Schachermayer and Tschiderer for conservative diffusions. Extensions are developed to general “convex divergences” and to countable state-spaces. The steepest descent and gradient flow properties for the variance, the relative entropy, and appropriate generalizations, are studied along with their respective geometries under conditions of detailed balance, leading to a very direct proof for the HWI inequality of Otto and Villani in the present context.","lang":"eng"}],"citation":{"ieee":"I. Karatzas, J. Maas, and W. Schachermayer, “Trajectorial dissipation and gradient flow for the relative entropy in Markov chains,” <i>Communications in Information and Systems</i>, vol. 21, no. 4. International Press, pp. 481–536, 2021.","apa":"Karatzas, I., Maas, J., &#38; Schachermayer, W. (2021). Trajectorial dissipation and gradient flow for the relative entropy in Markov chains. <i>Communications in Information and Systems</i>. International Press. <a href=\"https://doi.org/10.4310/CIS.2021.v21.n4.a1\">https://doi.org/10.4310/CIS.2021.v21.n4.a1</a>","chicago":"Karatzas, Ioannis, Jan Maas, and Walter Schachermayer. “Trajectorial Dissipation and Gradient Flow for the Relative Entropy in Markov Chains.” <i>Communications in Information and Systems</i>. International Press, 2021. <a href=\"https://doi.org/10.4310/CIS.2021.v21.n4.a1\">https://doi.org/10.4310/CIS.2021.v21.n4.a1</a>.","mla":"Karatzas, Ioannis, et al. “Trajectorial Dissipation and Gradient Flow for the Relative Entropy in Markov Chains.” <i>Communications in Information and Systems</i>, vol. 21, no. 4, International Press, 2021, pp. 481–536, doi:<a href=\"https://doi.org/10.4310/CIS.2021.v21.n4.a1\">10.4310/CIS.2021.v21.n4.a1</a>.","ama":"Karatzas I, Maas J, Schachermayer W. Trajectorial dissipation and gradient flow for the relative entropy in Markov chains. <i>Communications in Information and Systems</i>. 2021;21(4):481-536. doi:<a href=\"https://doi.org/10.4310/CIS.2021.v21.n4.a1\">10.4310/CIS.2021.v21.n4.a1</a>","ista":"Karatzas I, Maas J, Schachermayer W. 2021. Trajectorial dissipation and gradient flow for the relative entropy in Markov chains. Communications in Information and Systems. 21(4), 481–536.","short":"I. Karatzas, J. Maas, W. Schachermayer, Communications in Information and Systems 21 (2021) 481–536."},"publication_status":"published","date_created":"2021-09-19T08:53:19Z","department":[{"_id":"JaMa"}],"language":[{"iso":"eng"}],"publisher":"International Press","article_type":"original","date_published":"2021-06-04T00:00:00Z","month":"06","page":"481-536","publication":"Communications in Information and Systems","issue":"4","status":"public","intvolume":"        21","type":"journal_article","day":"04"},{"file_date_updated":"2022-05-13T07:55:50Z","page":"124-158","publication":"Stochastic Processes and their Applications","type":"journal_article","day":"27","status":"public","intvolume":"       142","department":[{"_id":"JaMa"}],"has_accepted_license":"1","file":[{"access_level":"open_access","date_updated":"2022-05-13T07:55:50Z","file_size":2115791,"file_name":"2021_StochasticProcessesAppl_Floreani.pdf","checksum":"56768c553d7218ee5714902ffec90ec4","date_created":"2022-05-13T07:55:50Z","relation":"main_file","content_type":"application/pdf","file_id":"11370","creator":"dernst","success":1}],"date_created":"2021-09-19T22:01:25Z","article_type":"original","date_published":"2021-08-27T00:00:00Z","month":"08","language":[{"iso":"eng"}],"scopus_import":"1","publisher":"Elsevier","article_processing_charge":"Yes","oa":1,"volume":142,"date_updated":"2023-08-14T06:52:43Z","arxiv":1,"project":[{"grant_number":"754411","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships"}],"quality_controlled":"1","oa_version":"Published Version","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","acknowledgement":"The authors would like to thank Marek Biskup and Alberto Chiarini for useful suggestions and  Cristian  Giardina,  Frank  den  Hollander  and  Shubhamoy  Nandan  for  inspiring  discussions.  S.F.  acknowledges  Simona  Villa  for  her  help  in  creating  the  picture.  Furthermore, the  authors  thank  two  anonymous  referees  for  the  careful  reading  of  the  manuscript.  S.F. acknowledges  financial  support  from  NWO,  The  Netherlands  via  the  grant  TOP1.17.019. F.S.  acknowledges  financial  support  from  NWO  via  the  TOP1  grant  613.001.552  as  well  as funding from the European Union’s Horizon 2020 research and innovation programme under the Marie-Skłodowska-Curie grant agreement No. 754411.","publication_identifier":{"issn":["0304-4149"]},"_id":"10024","citation":{"mla":"Floreani, Simone, et al. “Hydrodynamics for the Partial Exclusion Process in Random Environment.” <i>Stochastic Processes and Their Applications</i>, vol. 142, Elsevier, 2021, pp. 124–58, doi:<a href=\"https://doi.org/10.1016/j.spa.2021.08.006\">10.1016/j.spa.2021.08.006</a>.","ama":"Floreani S, Redig F, Sau F. Hydrodynamics for the partial exclusion process in random environment. <i>Stochastic Processes and their Applications</i>. 2021;142:124-158. doi:<a href=\"https://doi.org/10.1016/j.spa.2021.08.006\">10.1016/j.spa.2021.08.006</a>","short":"S. Floreani, F. Redig, F. Sau, Stochastic Processes and Their Applications 142 (2021) 124–158.","ista":"Floreani S, Redig F, Sau F. 2021. Hydrodynamics for the partial exclusion process in random environment. Stochastic Processes and their Applications. 142, 124–158.","ieee":"S. Floreani, F. Redig, and F. Sau, “Hydrodynamics for the partial exclusion process in random environment,” <i>Stochastic Processes and their Applications</i>, vol. 142. Elsevier, pp. 124–158, 2021.","apa":"Floreani, S., Redig, F., &#38; Sau, F. (2021). Hydrodynamics for the partial exclusion process in random environment. <i>Stochastic Processes and Their Applications</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.spa.2021.08.006\">https://doi.org/10.1016/j.spa.2021.08.006</a>","chicago":"Floreani, Simone, Frank Redig, and Federico Sau. “Hydrodynamics for the Partial Exclusion Process in Random Environment.” <i>Stochastic Processes and Their Applications</i>. Elsevier, 2021. <a href=\"https://doi.org/10.1016/j.spa.2021.08.006\">https://doi.org/10.1016/j.spa.2021.08.006</a>."},"publication_status":"published","author":[{"last_name":"Floreani","full_name":"Floreani, Simone","first_name":"Simone"},{"full_name":"Redig, Frank","last_name":"Redig","first_name":"Frank"},{"id":"E1836206-9F16-11E9-8814-AEFDE5697425","first_name":"Federico","full_name":"Sau, Federico","last_name":"Sau"}],"keyword":["hydrodynamic limit","random environment","random conductance model","arbitrary starting point quenched invariance principle","duality","mild solution"],"abstract":[{"lang":"eng","text":"In this paper, we introduce a random environment for the exclusion process in  obtained by assigning a maximal occupancy to each site. This maximal occupancy is allowed to randomly vary among sites, and partial exclusion occurs. Under the assumption of ergodicity under translation and uniform ellipticity of the environment, we derive a quenched hydrodynamic limit in path space by strengthening the mild solution approach initiated in Nagy (2002) and Faggionato (2007). To this purpose, we prove, employing the technology developed for the random conductance model, a homogenization result in the form of an arbitrary starting point quenched invariance principle for a single particle in the same environment, which is a result of independent interest. The self-duality property of the partial exclusion process allows us to transfer this homogenization result to the particle system and, then, apply the tightness criterion in Redig et al. (2020)."}],"isi":1,"tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"ddc":["519"],"ec_funded":1,"year":"2021","doi":"10.1016/j.spa.2021.08.006","title":"Hydrodynamics for the partial exclusion process in random environment","external_id":{"arxiv":["1911.12564"],"isi":["000697748500005"]}},{"oa_version":"Published Version","project":[{"call_identifier":"FWF","name":"Dissipation and Dispersion in Nonlinear Partial Differential Equations","_id":"260788DE-B435-11E9-9278-68D0E5697425"},{"grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems"}],"acknowledgement":"The author gratefully acknowledges support by the Austrian Science Fund (FWF), grants No W1245.","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","publication_identifier":{"issn":["2663-337X"]},"_id":"10030","article_processing_charge":"No","oa":1,"date_updated":"2023-09-07T13:31:06Z","author":[{"id":"30AD2CBC-F248-11E8-B48F-1D18A9856A87","first_name":"Lorenzo","full_name":"Portinale, Lorenzo","last_name":"Portinale"}],"abstract":[{"text":"This PhD thesis is primarily focused on the study of discrete transport problems, introduced for the first time in the seminal works of Maas [Maa11] and Mielke [Mie11] on finite state Markov chains and reaction-diffusion equations, respectively. More in detail, my research focuses on the study of transport costs on graphs, in particular the convergence and the stability of such problems in the discrete-to-continuum limit. This thesis also includes some results concerning\r\nnon-commutative optimal transport. The first chapter of this thesis consists of a general introduction to the optimal transport problems, both in the discrete, the continuous, and the non-commutative setting. Chapters 2 and 3 present the content of two works, obtained in collaboration with Peter Gladbach, Eva Kopfer, and Jan Maas, where we have been able to show the convergence of discrete transport costs on periodic graphs to suitable continuous ones, which can be described by means of a homogenisation result. We first focus on the particular case of quadratic costs on the real line and then extending the result to more general costs in arbitrary dimension. Our results are the first complete characterisation of limits of transport costs on periodic graphs in arbitrary dimension which do not rely on any additional symmetry. In Chapter 4 we turn our attention to one of the intriguing connection between evolution equations and optimal transport, represented by the theory of gradient flows. We show that discrete gradient flow structures associated to a finite volume approximation of a certain class of diffusive equations (Fokker–Planck) is stable in the limit of vanishing meshes, reproving the convergence of the scheme via the method of evolutionary Γ-convergence and exploiting a more variational point of view on the problem. This is based on a collaboration with Dominik Forkert and Jan Maas. Chapter 5 represents a change of perspective, moving away from the discrete world and reaching the non-commutative one. As in the discrete case, we discuss how classical tools coming from the commutative optimal transport can be translated into the setting of density matrices. In particular, in this final chapter we present a non-commutative version of the Schrödinger problem (or entropic regularised optimal transport problem) and discuss existence and characterisation of minimisers, a duality result, and present a non-commutative version of the well-known Sinkhorn algorithm to compute the above mentioned optimisers. This is based on a joint work with Dario Feliciangeli and Augusto Gerolin. Finally, Appendix A and B contain some additional material and discussions, with particular attention to Harnack inequalities and the regularity of flows on discrete spaces.","lang":"eng"}],"citation":{"apa":"Portinale, L. (2021). <i>Discrete-to-continuum limits of transport problems and gradient flows in the space of measures</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/at:ista:10030\">https://doi.org/10.15479/at:ista:10030</a>","ieee":"L. Portinale, “Discrete-to-continuum limits of transport problems and gradient flows in the space of measures,” Institute of Science and Technology Austria, 2021.","chicago":"Portinale, Lorenzo. “Discrete-to-Continuum Limits of Transport Problems and Gradient Flows in the Space of Measures.” Institute of Science and Technology Austria, 2021. <a href=\"https://doi.org/10.15479/at:ista:10030\">https://doi.org/10.15479/at:ista:10030</a>.","mla":"Portinale, Lorenzo. <i>Discrete-to-Continuum Limits of Transport Problems and Gradient Flows in the Space of Measures</i>. Institute of Science and Technology Austria, 2021, doi:<a href=\"https://doi.org/10.15479/at:ista:10030\">10.15479/at:ista:10030</a>.","ama":"Portinale L. Discrete-to-continuum limits of transport problems and gradient flows in the space of measures. 2021. doi:<a href=\"https://doi.org/10.15479/at:ista:10030\">10.15479/at:ista:10030</a>","short":"L. Portinale, Discrete-to-Continuum Limits of Transport Problems and Gradient Flows in the Space of Measures, Institute of Science and Technology Austria, 2021.","ista":"Portinale L. 2021. Discrete-to-continuum limits of transport problems and gradient flows in the space of measures. Institute of Science and Technology Austria."},"publication_status":"published","ddc":["515"],"related_material":{"record":[{"status":"public","id":"10022","relation":"part_of_dissertation"},{"id":"9792","relation":"part_of_dissertation","status":"public"},{"status":"public","relation":"part_of_dissertation","id":"7573"}]},"tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"alternative_title":["ISTA Thesis"],"title":"Discrete-to-continuum limits of transport problems and gradient flows in the space of measures","doi":"10.15479/at:ista:10030","year":"2021","acknowledged_ssus":[{"_id":"M-Shop"},{"_id":"NanoFab"}],"file_date_updated":"2022-03-10T12:14:42Z","supervisor":[{"orcid":"0000-0002-0845-1338","full_name":"Maas, Jan","last_name":"Maas","first_name":"Jan","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87"}],"status":"public","type":"dissertation","day":"22","date_created":"2021-09-21T09:14:15Z","file":[{"content_type":"application/x-zip-compressed","relation":"source_file","creator":"cchlebak","file_id":"10032","file_name":"tex_and_pictures.zip","file_size":3876668,"date_created":"2021-09-21T09:17:34Z","checksum":"8cd60dcb8762e8f21867e21e8001e183","date_updated":"2022-03-10T12:14:42Z","access_level":"closed"},{"creator":"cchlebak","file_id":"10047","relation":"main_file","content_type":"application/pdf","access_level":"open_access","date_updated":"2021-09-27T11:14:31Z","checksum":"9789e9d967c853c1503ec7f307170279","date_created":"2021-09-27T11:14:31Z","file_size":2532673,"file_name":"thesis_portinale_Final (1).pdf"}],"department":[{"_id":"GradSch"},{"_id":"JaMa"}],"has_accepted_license":"1","degree_awarded":"PhD","language":[{"iso":"eng"}],"publisher":"Institute of Science and Technology Austria","date_published":"2021-09-22T00:00:00Z","month":"09"},{"day":"15","type":"journal_article","intvolume":"       281","status":"public","issue":"11","publication":"Journal of Functional Analysis","month":"09","date_published":"2021-09-15T00:00:00Z","article_type":"original","publisher":"Elsevier","scopus_import":"1","language":[{"iso":"eng"}],"department":[{"_id":"JaMa"}],"date_created":"2021-10-03T22:01:21Z","publication_status":"published","citation":{"mla":"Dello Schiavo, Lorenzo, and Kohei Suzuki. “Rademacher-Type Theorems and Sobolev-to-Lipschitz Properties for Strongly Local Dirichlet Spaces.” <i>Journal of Functional Analysis</i>, vol. 281, no. 11, 109234, Elsevier, 2021, doi:<a href=\"https://doi.org/10.1016/j.jfa.2021.109234\">10.1016/j.jfa.2021.109234</a>.","ama":"Dello Schiavo L, Suzuki K. Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local Dirichlet spaces. <i>Journal of Functional Analysis</i>. 2021;281(11). doi:<a href=\"https://doi.org/10.1016/j.jfa.2021.109234\">10.1016/j.jfa.2021.109234</a>","short":"L. Dello Schiavo, K. Suzuki, Journal of Functional Analysis 281 (2021).","ista":"Dello Schiavo L, Suzuki K. 2021. Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local Dirichlet spaces. Journal of Functional Analysis. 281(11), 109234.","apa":"Dello Schiavo, L., &#38; Suzuki, K. (2021). Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local Dirichlet spaces. <i>Journal of Functional Analysis</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jfa.2021.109234\">https://doi.org/10.1016/j.jfa.2021.109234</a>","ieee":"L. Dello Schiavo and K. Suzuki, “Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local Dirichlet spaces,” <i>Journal of Functional Analysis</i>, vol. 281, no. 11. Elsevier, 2021.","chicago":"Dello Schiavo, Lorenzo, and Kohei Suzuki. “Rademacher-Type Theorems and Sobolev-to-Lipschitz Properties for Strongly Local Dirichlet Spaces.” <i>Journal of Functional Analysis</i>. Elsevier, 2021. <a href=\"https://doi.org/10.1016/j.jfa.2021.109234\">https://doi.org/10.1016/j.jfa.2021.109234</a>."},"abstract":[{"lang":"eng","text":"We extensively discuss the Rademacher and Sobolev-to-Lipschitz properties for generalized intrinsic distances on strongly local Dirichlet spaces possibly without square field operator. We present many non-smooth and infinite-dimensional examples. As an application, we prove the integral Varadhan short-time asymptotic with respect to a given distance function for a large class of strongly local Dirichlet forms."}],"author":[{"full_name":"Dello Schiavo, Lorenzo","last_name":"Dello Schiavo","orcid":"0000-0002-9881-6870","first_name":"Lorenzo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E"},{"last_name":"Suzuki","full_name":"Suzuki, Kohei","first_name":"Kohei"}],"arxiv":1,"volume":281,"oa":1,"date_updated":"2023-08-14T07:05:44Z","article_processing_charge":"No","_id":"10070","publication_identifier":{"eissn":["1096-0783"],"issn":["0022-1236"]},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","acknowledgement":"The authors are grateful to Professor Kazuhiro Kuwae for kindly providing a copy of [49]. They are also grateful to Dr. Bang-Xian Han for helpful discussions on the Sobolev-to-Lipschitz property on metric measure spaces. They wish to express their deepest gratitude to an anonymous Reviewer, whose punctual remarks and comments greatly improved the accessibility and overall quality of the initial submission. This work was completed while L.D.S. was a member of the Institut für Angewandte Mathematik of the University of Bonn. He acknowledges funding of his position at that time by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through the Sonderforschungsbereich (Sfb, Collaborative Research Center) 1060 - project number 211504053. He also acknowledges funding of his current position by the Austrian Science Fund (FWF) grant F65, and by the European Research Council (ERC, grant No. 716117, awarded to Prof. Dr. Jan Maas). K.S. gratefully acknowledges funding by: the JSPS Overseas Research Fellowships, Grant Nr. 290142; World Premier International Research Center Initiative (WPI), MEXT, Japan; and JSPS Grant-in-Aid for Scientific Research on Innovative Areas “Discrete Geometric Analysis for Materials Design”, Grant Number 17H06465.","quality_controlled":"1","oa_version":"Preprint","project":[{"grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems"},{"grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425","name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020"}],"doi":"10.1016/j.jfa.2021.109234","year":"2021","ec_funded":1,"title":"Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local Dirichlet spaces","external_id":{"arxiv":["2008.01492"],"isi":["000703896600005"]},"isi":1,"article_number":"109234","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2008.01492","open_access":"1"}]},{"page":"339-380","publication":"Markov Processes And Related Fields","issue":"3","status":"public","intvolume":"        27","type":"journal_article","day":"16","date_created":"2022-01-10T14:02:31Z","department":[{"_id":"JaMa"}],"language":[{"iso":"eng"}],"publisher":"Polymat Publishing","article_type":"original","date_published":"2021-03-16T00:00:00Z","month":"03","project":[{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"quality_controlled":"1","oa_version":"Preprint","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","acknowledgement":"F.S. would like to thank Mario Ayala and Frank Redig for useful discussions. J.P.C. acknowledges partial financial support from the US National Science Foundation (DMS-1855604). F.S. was financially supported by the European Union’s Horizon 2020 research and innovation programme under the Marie-Skłodowska-Curie grant agreement No. 754411.\r\n","publication_identifier":{"issn":["1024-2953"]},"_id":"10613","article_processing_charge":"No","oa":1,"volume":27,"date_updated":"2022-01-10T15:29:08Z","arxiv":1,"author":[{"first_name":"Joe P.","full_name":"Chen, Joe P.","last_name":"Chen"},{"id":"E1836206-9F16-11E9-8814-AEFDE5697425","first_name":"Federico","last_name":"Sau","full_name":"Sau, Federico"}],"keyword":["interacting particle systems","higher-order fields","hydrodynamic limit","equilibrium fluctuations","duality"],"abstract":[{"lang":"eng","text":"Motivated by the recent preprint [\\emph{arXiv:2004.08412}] by Ayala, Carinci, and Redig, we first provide a general framework for the study of scaling limits of higher-order fields. Then, by considering the same class of infinite interacting particle systems as in [\\emph{arXiv:2004.08412}], namely symmetric simple exclusion and inclusion processes in the d-dimensional Euclidean lattice, we prove the hydrodynamic limit, and convergence for the equilibrium fluctuations, of higher-order fields. In particular, the limit fields exhibit a tensor structure. Our fluctuation result differs from that in [\\emph{arXiv:2004.08412}], since we considered-dimensional Euclidean lattice, we prove the hydrodynamic limit, and convergence for the equilibrium fluctuations, of higher-order fields. In particular, the limit fields exhibit a tensor structure. Our fluctuation result differs from that in [\\emph{arXiv:2004.08412}], since we consider a different notion of higher-order fluctuation fields."}],"citation":{"ista":"Chen JP, Sau F. 2021. Higher-order hydrodynamics and equilibrium fluctuations of interacting particle systems. Markov Processes And Related Fields. 27(3), 339–380.","short":"J.P. Chen, F. Sau, Markov Processes And Related Fields 27 (2021) 339–380.","ama":"Chen JP, Sau F. Higher-order hydrodynamics and equilibrium fluctuations of interacting particle systems. <i>Markov Processes And Related Fields</i>. 2021;27(3):339-380.","mla":"Chen, Joe P., and Federico Sau. “Higher-Order Hydrodynamics and Equilibrium Fluctuations of Interacting Particle Systems.” <i>Markov Processes And Related Fields</i>, vol. 27, no. 3, Polymat Publishing, 2021, pp. 339–80.","chicago":"Chen, Joe P., and Federico Sau. “Higher-Order Hydrodynamics and Equilibrium Fluctuations of Interacting Particle Systems.” <i>Markov Processes And Related Fields</i>. Polymat Publishing, 2021.","ieee":"J. P. Chen and F. Sau, “Higher-order hydrodynamics and equilibrium fluctuations of interacting particle systems,” <i>Markov Processes And Related Fields</i>, vol. 27, no. 3. Polymat Publishing, pp. 339–380, 2021.","apa":"Chen, J. P., &#38; Sau, F. (2021). Higher-order hydrodynamics and equilibrium fluctuations of interacting particle systems. <i>Markov Processes And Related Fields</i>. Polymat Publishing."},"publication_status":"published","related_material":{"link":[{"relation":"other","description":"Link to Abstract on publisher's website","url":"http://math-mprf.org/journal/articles/id1614/"},{"url":"https://arxiv.org/abs/2004.08412","relation":"used_for_analysis_in","description":"Referred to in Abstract"}]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2008.13403"}],"title":"Higher-order hydrodynamics and equilibrium fluctuations of interacting particle systems","external_id":{"arxiv":["2008.13403"]},"ec_funded":1,"year":"2021"},{"alternative_title":["ISTA Thesis"],"tmp":{"name":"Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0)","short":"CC BY-ND (4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nd/4.0/legalcode","image":"/image/cc_by_nd.png"},"ddc":["515","519","539"],"related_material":{"record":[{"id":"9787","relation":"part_of_dissertation","status":"public"},{"status":"public","relation":"part_of_dissertation","id":"9792"},{"relation":"part_of_dissertation","id":"9225","status":"public"},{"id":"9781","relation":"part_of_dissertation","status":"public"},{"id":"9791","relation":"part_of_dissertation","status":"public"}]},"ec_funded":1,"doi":"10.15479/at:ista:9733","year":"2021","title":"The polaron at strong coupling","oa":1,"date_updated":"2024-03-06T12:30:44Z","article_processing_charge":"No","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","oa_version":"Published Version","project":[{"grant_number":"716117","call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425"},{"call_identifier":"H2020","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","name":"Analysis of quantum many-body systems","grant_number":"694227"},{"grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems"}],"_id":"9733","publication_identifier":{"issn":["2663-337X"]},"publication_status":"published","citation":{"chicago":"Feliciangeli, Dario. “The Polaron at Strong Coupling.” Institute of Science and Technology Austria, 2021. <a href=\"https://doi.org/10.15479/at:ista:9733\">https://doi.org/10.15479/at:ista:9733</a>.","apa":"Feliciangeli, D. (2021). <i>The polaron at strong coupling</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/at:ista:9733\">https://doi.org/10.15479/at:ista:9733</a>","ieee":"D. Feliciangeli, “The polaron at strong coupling,” Institute of Science and Technology Austria, 2021.","short":"D. Feliciangeli, The Polaron at Strong Coupling, Institute of Science and Technology Austria, 2021.","ista":"Feliciangeli D. 2021. The polaron at strong coupling. Institute of Science and Technology Austria.","ama":"Feliciangeli D. The polaron at strong coupling. 2021. doi:<a href=\"https://doi.org/10.15479/at:ista:9733\">10.15479/at:ista:9733</a>","mla":"Feliciangeli, Dario. <i>The Polaron at Strong Coupling</i>. Institute of Science and Technology Austria, 2021, doi:<a href=\"https://doi.org/10.15479/at:ista:9733\">10.15479/at:ista:9733</a>."},"author":[{"orcid":"0000-0003-0754-8530","last_name":"Feliciangeli","full_name":"Feliciangeli, Dario","first_name":"Dario","id":"41A639AA-F248-11E8-B48F-1D18A9856A87"}],"abstract":[{"text":"This thesis is the result of the research carried out by the author during his PhD at IST Austria between 2017 and 2021. It mainly focuses on the Fröhlich polaron model, specifically to its regime of strong coupling. This model, which is rigorously introduced and discussed in the introduction, has been of great interest in condensed matter physics and field theory for more than eighty years. It is used to describe an electron interacting with the atoms of a solid material (the strength of this interaction is modeled by the presence of a coupling constant α in the Hamiltonian of the system). The particular regime examined here, which is mathematically described by considering the limit α →∞, displays many interesting features related to the emergence of classical behavior, which allows for a simplified effective description of the system under analysis. The properties, the range of validity and a quantitative analysis of the precision of such classical approximations are the main object of the present work. We specify our investigation to the study of the ground state energy of the system, its dynamics and its effective mass. For each of these problems, we provide in the introduction an overview of the previously known results and a detailed account of the original contributions by the author.","lang":"eng"}],"department":[{"_id":"GradSch"},{"_id":"RoSe"},{"_id":"JaMa"}],"license":"https://creativecommons.org/licenses/by-nd/4.0/","has_accepted_license":"1","degree_awarded":"PhD","date_created":"2021-07-27T15:48:30Z","file":[{"date_created":"2021-08-19T14:03:48Z","checksum":"e88bb8ca43948abe060eb2d2fa719881","file_name":"Thesis_FeliciangeliA.pdf","file_size":1958710,"date_updated":"2021-09-06T09:28:56Z","access_level":"open_access","creator":"dfelicia","file_id":"9944","content_type":"application/pdf","relation":"main_file"},{"relation":"source_file","content_type":"application/octet-stream","creator":"dfelicia","file_id":"9945","file_size":3771669,"file_name":"thesis.7z","checksum":"72810843abee83705853505b3f8348aa","date_created":"2021-08-19T14:06:35Z","access_level":"closed","date_updated":"2022-03-10T12:13:57Z"}],"date_published":"2021-08-20T00:00:00Z","month":"08","language":[{"iso":"eng"}],"publisher":"Institute of Science and Technology Austria","file_date_updated":"2022-03-10T12:13:57Z","page":"180","type":"dissertation","day":"20","supervisor":[{"orcid":"0000-0002-6781-0521","last_name":"Seiringer","full_name":"Seiringer, Robert","first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Maas","full_name":"Maas, Jan","orcid":"0000-0002-0845-1338","first_name":"Jan","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87"}],"status":"public"},{"ec_funded":1,"doi":"10.48550/arXiv.2106.11217","year":"2021","title":"A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature","external_id":{"arxiv":["2106.11217"]},"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2106.11217"}],"article_number":"2106.11217","tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"ddc":["510"],"related_material":{"record":[{"id":"9733","relation":"dissertation_contains","status":"public"},{"status":"public","id":"10030","relation":"dissertation_contains"},{"status":"public","id":"12911","relation":"later_version"}]},"publication_status":"submitted","citation":{"ista":"Feliciangeli D, Gerolin A, Portinale L. A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature. arXiv, 2106.11217.","short":"D. Feliciangeli, A. Gerolin, L. Portinale, ArXiv (n.d.).","mla":"Feliciangeli, Dario, et al. “A Non-Commutative Entropic Optimal Transport Approach to Quantum Composite Systems at Positive Temperature.” <i>ArXiv</i>, 2106.11217, doi:<a href=\"https://doi.org/10.48550/arXiv.2106.11217\">10.48550/arXiv.2106.11217</a>.","ama":"Feliciangeli D, Gerolin A, Portinale L. A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2106.11217\">10.48550/arXiv.2106.11217</a>","chicago":"Feliciangeli, Dario, Augusto Gerolin, and Lorenzo Portinale. “A Non-Commutative Entropic Optimal Transport Approach to Quantum Composite Systems at Positive Temperature.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2106.11217\">https://doi.org/10.48550/arXiv.2106.11217</a>.","apa":"Feliciangeli, D., Gerolin, A., &#38; Portinale, L. (n.d.). A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2106.11217\">https://doi.org/10.48550/arXiv.2106.11217</a>","ieee":"D. Feliciangeli, A. Gerolin, and L. Portinale, “A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature,” <i>arXiv</i>. ."},"author":[{"full_name":"Feliciangeli, Dario","last_name":"Feliciangeli","orcid":"0000-0003-0754-8530","first_name":"Dario","id":"41A639AA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Augusto","full_name":"Gerolin, Augusto","last_name":"Gerolin"},{"last_name":"Portinale","full_name":"Portinale, Lorenzo","first_name":"Lorenzo","id":"30AD2CBC-F248-11E8-B48F-1D18A9856A87"}],"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 careful 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"}],"oa":1,"date_updated":"2023-11-14T13:21:01Z","article_processing_charge":"No","arxiv":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","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 thanks 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. Finally, the authors also thanks J. Maas and R. Seiringer for their feedback and useful comments to a first draft of the article.  L.P. acknowledges support by the Austrian Science Fund (FWF), grants No W1245 and NoF65. D.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 European Research Council under H2020/MSCA-IF “OTmeetsDFT” [grant ID: 795942].","oa_version":"Preprint","project":[{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","name":"Analysis of quantum many-body systems","call_identifier":"H2020","grant_number":"694227"},{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020","grant_number":"716117"},{"grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems"}],"_id":"9792","date_published":"2021-07-21T00:00:00Z","month":"07","language":[{"iso":"eng"}],"department":[{"_id":"RoSe"},{"_id":"JaMa"}],"has_accepted_license":"1","date_created":"2021-08-06T09:07:12Z","type":"preprint","day":"21","status":"public","publication":"arXiv"},{"abstract":[{"text":"In this article we introduce a complete gradient estimate for symmetric quantum Markov semigroups on von Neumann algebras equipped with a normal faithful tracial state, which implies semi-convexity of the entropy with respect to the recently introduced noncommutative 2-Wasserstein distance. We show that this complete gradient estimate is stable under tensor products and free products and establish its validity for a number of examples. As an application we prove a complete modified logarithmic Sobolev inequality with optimal constant for Poisson-type semigroups on free group factors.","lang":"eng"}],"author":[{"id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","orcid":"0000-0002-0519-4241","full_name":"Wirth, Melchior","last_name":"Wirth","first_name":"Melchior"},{"id":"D8F41E38-9E66-11E9-A9E2-65C2E5697425","last_name":"Zhang","full_name":"Zhang, Haonan","first_name":"Haonan"}],"keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"citation":{"ieee":"M. Wirth and H. Zhang, “Complete gradient estimates of quantum Markov semigroups,” <i>Communications in Mathematical Physics</i>, vol. 387. Springer Nature, pp. 761–791, 2021.","apa":"Wirth, M., &#38; Zhang, H. (2021). Complete gradient estimates of quantum Markov semigroups. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-021-04199-4\">https://doi.org/10.1007/s00220-021-04199-4</a>","chicago":"Wirth, Melchior, and Haonan Zhang. “Complete Gradient Estimates of Quantum Markov Semigroups.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00220-021-04199-4\">https://doi.org/10.1007/s00220-021-04199-4</a>.","ama":"Wirth M, Zhang H. Complete gradient estimates of quantum Markov semigroups. <i>Communications in Mathematical Physics</i>. 2021;387:761–791. doi:<a href=\"https://doi.org/10.1007/s00220-021-04199-4\">10.1007/s00220-021-04199-4</a>","mla":"Wirth, Melchior, and Haonan Zhang. “Complete Gradient Estimates of Quantum Markov Semigroups.” <i>Communications in Mathematical Physics</i>, vol. 387, Springer Nature, 2021, pp. 761–791, doi:<a href=\"https://doi.org/10.1007/s00220-021-04199-4\">10.1007/s00220-021-04199-4</a>.","short":"M. Wirth, H. Zhang, Communications in Mathematical Physics 387 (2021) 761–791.","ista":"Wirth M, Zhang H. 2021. Complete gradient estimates of quantum Markov semigroups. Communications in Mathematical Physics. 387, 761–791."},"publication_status":"published","publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"_id":"9973","oa_version":"Published Version","project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"},{"grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020"},{"grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems"}],"quality_controlled":"1","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","acknowledgement":"Both authors would like to thank Jan Maas for fruitful discussions and helpful comments.","arxiv":1,"article_processing_charge":"Yes (via OA deal)","volume":387,"oa":1,"date_updated":"2023-08-11T11:09:07Z","title":"Complete gradient estimates of quantum Markov semigroups","external_id":{"arxiv":["2007.13506"],"isi":["000691214200001"]},"year":"2021","doi":"10.1007/s00220-021-04199-4","ec_funded":1,"ddc":["621"],"tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"isi":1,"intvolume":"       387","status":"public","day":"30","type":"journal_article","publication":"Communications in Mathematical Physics","page":"761–791","file_date_updated":"2021-09-08T09:46:34Z","scopus_import":"1","publisher":"Springer Nature","language":[{"iso":"eng"}],"month":"08","article_type":"original","date_published":"2021-08-30T00:00:00Z","file":[{"date_updated":"2021-09-08T09:46:34Z","access_level":"open_access","file_name":"2021_CommunMathPhys_Wirth.pdf","file_size":505971,"date_created":"2021-09-08T07:34:24Z","checksum":"8a602f916b1c2b0dc1159708b7cb204b","content_type":"application/pdf","relation":"main_file","creator":"cchlebak","file_id":"9990"}],"date_created":"2021-08-30T10:07:44Z","has_accepted_license":"1","department":[{"_id":"JaMa"}]},{"article_processing_charge":"No","volume":61,"oa":1,"date_updated":"2023-08-22T10:32:29Z","arxiv":1,"oa_version":"Preprint","quality_controlled":"1","project":[{"grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","acknowledgement":"This research was supported by the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant Agreement No. 754411. The author would like to thank Anna Vershynina and Sarah Chehade for their helpful comments.","publication_identifier":{"issn":["00222488"]},"_id":"8670","citation":{"ieee":"H. Zhang, “Equality conditions of data processing inequality for α-z Rényi relative entropies,” <i>Journal of Mathematical Physics</i>, vol. 61, no. 10. AIP Publishing, 2020.","apa":"Zhang, H. (2020). Equality conditions of data processing inequality for α-z Rényi relative entropies. <i>Journal of Mathematical Physics</i>. AIP Publishing. <a href=\"https://doi.org/10.1063/5.0022787\">https://doi.org/10.1063/5.0022787</a>","chicago":"Zhang, Haonan. “Equality Conditions of Data Processing Inequality for α-z Rényi Relative Entropies.” <i>Journal of Mathematical Physics</i>. AIP Publishing, 2020. <a href=\"https://doi.org/10.1063/5.0022787\">https://doi.org/10.1063/5.0022787</a>.","ama":"Zhang H. Equality conditions of data processing inequality for α-z Rényi relative entropies. <i>Journal of Mathematical Physics</i>. 2020;61(10). doi:<a href=\"https://doi.org/10.1063/5.0022787\">10.1063/5.0022787</a>","mla":"Zhang, Haonan. “Equality Conditions of Data Processing Inequality for α-z Rényi Relative Entropies.” <i>Journal of Mathematical Physics</i>, vol. 61, no. 10, 102201, AIP Publishing, 2020, doi:<a href=\"https://doi.org/10.1063/5.0022787\">10.1063/5.0022787</a>.","short":"H. Zhang, Journal of Mathematical Physics 61 (2020).","ista":"Zhang H. 2020. Equality conditions of data processing inequality for α-z Rényi relative entropies. Journal of Mathematical Physics. 61(10), 102201."},"publication_status":"published","author":[{"id":"D8F41E38-9E66-11E9-A9E2-65C2E5697425","first_name":"Haonan","last_name":"Zhang","full_name":"Zhang, Haonan"}],"abstract":[{"lang":"eng","text":"The α–z Rényi relative entropies are a two-parameter family of Rényi relative entropies that are quantum generalizations of the classical α-Rényi relative entropies. In the work [Adv. Math. 365, 107053 (2020)], we decided the full range of (α, z) for which the data processing inequality (DPI) is valid. In this paper, we give algebraic conditions for the equality in DPI. For the full range of parameters (α, z), we give necessary conditions and sufficient conditions. For most parameters, we give equivalent conditions. This generalizes and strengthens the results of Leditzky et al. [Lett. Math. Phys. 107, 61–80 (2017)]."}],"main_file_link":[{"url":"https://arxiv.org/abs/2007.06644","open_access":"1"}],"article_number":"102201","isi":1,"ec_funded":1,"year":"2020","doi":"10.1063/5.0022787","external_id":{"isi":["000578529200001"],"arxiv":["2007.06644"]},"title":"Equality conditions of data processing inequality for α-z Rényi relative entropies","publication":"Journal of Mathematical Physics","issue":"10","type":"journal_article","day":"01","status":"public","intvolume":"        61","department":[{"_id":"JaMa"}],"date_created":"2020-10-18T22:01:36Z","article_type":"original","date_published":"2020-10-01T00:00:00Z","month":"10","language":[{"iso":"eng"}],"scopus_import":"1","publisher":"AIP Publishing"},{"intvolume":"       181","status":"public","day":"01","type":"journal_article","publication":"Journal of Statistical Physics","issue":"6","page":"2257-2303","file_date_updated":"2021-02-04T10:29:11Z","scopus_import":"1","publisher":"Springer Nature","language":[{"iso":"eng"}],"month":"12","article_type":"original","date_published":"2020-12-01T00:00:00Z","date_created":"2020-11-15T23:01:18Z","file":[{"creator":"dernst","file_id":"9087","relation":"main_file","content_type":"application/pdf","success":1,"access_level":"open_access","date_updated":"2021-02-04T10:29:11Z","checksum":"bc2b63a90197b97cbc73eccada4639f5","date_created":"2021-02-04T10:29:11Z","file_size":753596,"file_name":"2020_JourStatPhysics_Maas.pdf"}],"has_accepted_license":"1","department":[{"_id":"JaMa"}],"abstract":[{"text":"We consider various modeling levels for spatially homogeneous chemical reaction systems, namely the chemical master equation, the chemical Langevin dynamics, and the reaction-rate equation. Throughout we restrict our study to the case where the microscopic system satisfies the detailed-balance condition. The latter allows us to enrich the systems with a gradient structure, i.e. the evolution is given by a gradient-flow equation. We present the arising links between the associated gradient structures that are driven by the relative entropy of the detailed-balance steady state. The limit of large volumes is studied in the sense of evolutionary Γ-convergence of gradient flows. Moreover, we use the gradient structures to derive hybrid models for coupling different modeling levels.","lang":"eng"}],"author":[{"orcid":"0000-0002-0845-1338","last_name":"Maas","full_name":"Maas, Jan","first_name":"Jan","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Mielke, Alexander","last_name":"Mielke","first_name":"Alexander"}],"citation":{"chicago":"Maas, Jan, and Alexander Mielke. “Modeling of Chemical Reaction Systems with Detailed Balance Using Gradient Structures.” <i>Journal of Statistical Physics</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s10955-020-02663-4\">https://doi.org/10.1007/s10955-020-02663-4</a>.","ieee":"J. Maas and A. Mielke, “Modeling of chemical reaction systems with detailed balance using gradient structures,” <i>Journal of Statistical Physics</i>, vol. 181, no. 6. Springer Nature, pp. 2257–2303, 2020.","apa":"Maas, J., &#38; Mielke, A. (2020). Modeling of chemical reaction systems with detailed balance using gradient structures. <i>Journal of Statistical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s10955-020-02663-4\">https://doi.org/10.1007/s10955-020-02663-4</a>","short":"J. Maas, A. Mielke, Journal of Statistical Physics 181 (2020) 2257–2303.","ista":"Maas J, Mielke A. 2020. Modeling of chemical reaction systems with detailed balance using gradient structures. Journal of Statistical Physics. 181(6), 2257–2303.","mla":"Maas, Jan, and Alexander Mielke. “Modeling of Chemical Reaction Systems with Detailed Balance Using Gradient Structures.” <i>Journal of Statistical Physics</i>, vol. 181, no. 6, Springer Nature, 2020, pp. 2257–303, doi:<a href=\"https://doi.org/10.1007/s10955-020-02663-4\">10.1007/s10955-020-02663-4</a>.","ama":"Maas J, Mielke A. Modeling of chemical reaction systems with detailed balance using gradient structures. <i>Journal of Statistical Physics</i>. 2020;181(6):2257-2303. doi:<a href=\"https://doi.org/10.1007/s10955-020-02663-4\">10.1007/s10955-020-02663-4</a>"},"publication_status":"published","publication_identifier":{"eissn":["15729613"],"issn":["00224715"]},"_id":"8758","quality_controlled":"1","project":[{"name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"716117"},{"grant_number":" F06504","call_identifier":"FWF","name":"Taming Complexity in Partial Di erential Systems","_id":"260482E2-B435-11E9-9278-68D0E5697425"}],"oa_version":"Published Version","acknowledgement":"The research of A.M. was partially supported by the Deutsche Forschungsgemeinschaft (DFG) via the Collaborative Research Center SFB 1114 Scaling Cascades in Complex Systems (Project No. 235221301), through the Subproject C05 Effective models for materials and interfaces with multiple scales. 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), and by the Austrian Science Fund (FWF), Project SFB F65. The authors thank Christof Schütte, Robert I. A. Patterson, and Stefanie Winkelmann for helpful and stimulating discussions. Open access funding provided by Austrian Science Fund (FWF).","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","arxiv":1,"article_processing_charge":"No","date_updated":"2023-08-22T13:24:27Z","volume":181,"oa":1,"title":"Modeling of chemical reaction systems with detailed balance using gradient structures","external_id":{"isi":["000587107200002"],"arxiv":["2004.02831"]},"year":"2020","doi":"10.1007/s10955-020-02663-4","ec_funded":1,"ddc":["510"],"tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"isi":1},{"publication":"Electronic Journal of Probability","file_date_updated":"2020-12-28T08:24:08Z","intvolume":"        25","status":"public","day":"21","type":"journal_article","date_created":"2020-12-27T23:01:17Z","file":[{"file_size":696653,"file_name":"2020_ElectronJProbab_Redig.pdf","checksum":"d75359b9814e78d57c0a481b7cde3751","date_created":"2020-12-28T08:24:08Z","access_level":"open_access","date_updated":"2020-12-28T08:24:08Z","success":1,"relation":"main_file","content_type":"application/pdf","file_id":"8976","creator":"dernst"}],"has_accepted_license":"1","department":[{"_id":"JaMa"}],"scopus_import":"1","publisher":" Institute of Mathematical Statistics","language":[{"iso":"eng"}],"month":"10","article_type":"original","date_published":"2020-10-21T00:00:00Z","publication_identifier":{"eissn":["1083-6489"]},"_id":"8973","oa_version":"Published Version","quality_controlled":"1","project":[{"call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","acknowledgement":"We warmly thank S.R.S. Varadhan for many enlightening discussions at an early stage of this work. We are indebted to Francesca Collet for fruitful discussions and constant support all throughout this work. We thank Simone Floreani\r\nand Alberto Chiarini for helpful conversations on the final part of this paper as well as both referees for their careful reading and for raising relevant issues on some weak points contained in a previous version of this manuscript; we believe this helped us to improve it.\r\nPart of this work was done during the authors’ stay at the Institut Henri Poincaré (UMS 5208 CNRS-Sorbonne Université) – Centre Emile Borel during the trimester Stochastic Dynamics Out of Equilibrium. The authors thank this institution for hospitality and support (through LabEx CARMIN, ANR-10-LABX-59-01). F.S. thanks laboratoire\r\nMAP5 of Université de Paris, and E.S. thanks Delft University, for financial support and hospitality. F.S. acknowledges NWO for financial support via the TOP1 grant 613.001.552 as well as funding from the European Union’s Horizon 2020 research and innovation programme under the Marie-Skłodowska-Curie grant agreement No. 754411. This research has been conducted within the FP2M federation (CNRS FR 2036).","arxiv":1,"article_processing_charge":"No","date_updated":"2023-10-17T12:51:56Z","volume":25,"oa":1,"abstract":[{"lang":"eng","text":"We consider the symmetric simple exclusion process in Zd with quenched bounded dynamic random conductances and prove its hydrodynamic limit in path space. The main tool is the connection, due to the self-duality of the process, between the invariance principle for single particles starting from all points and the macroscopic behavior of the density field. While the hydrodynamic limit at fixed macroscopic times is obtained via a generalization to the time-inhomogeneous context of the strategy introduced in [41], in order to prove tightness for the sequence of empirical density fields we develop a new criterion based on the notion of uniform conditional stochastic continuity, following [50]. In conclusion, we show that uniform elliptic dynamic conductances provide an example of environments in which the so-called arbitrary starting point invariance principle may be derived from the invariance principle of a single particle starting from the origin. Therefore, our hydrodynamics result applies to the examples of quenched environments considered in, e.g., [1], [3], [6] in combination with the hypothesis of uniform ellipticity."}],"author":[{"full_name":"Redig, Frank","last_name":"Redig","first_name":"Frank"},{"first_name":"Ellen","last_name":"Saada","full_name":"Saada, Ellen"},{"id":"E1836206-9F16-11E9-8814-AEFDE5697425","first_name":"Federico","last_name":"Sau","full_name":"Sau, Federico"}],"citation":{"chicago":"Redig, Frank, Ellen Saada, and Federico Sau. “Symmetric Simple Exclusion Process in Dynamic Environment: Hydrodynamics.” <i>Electronic Journal of Probability</i>.  Institute of Mathematical Statistics, 2020. <a href=\"https://doi.org/10.1214/20-EJP536\">https://doi.org/10.1214/20-EJP536</a>.","ieee":"F. Redig, E. Saada, and F. Sau, “Symmetric simple exclusion process in dynamic environment: Hydrodynamics,” <i>Electronic Journal of Probability</i>, vol. 25.  Institute of Mathematical Statistics, 2020.","apa":"Redig, F., Saada, E., &#38; Sau, F. (2020). Symmetric simple exclusion process in dynamic environment: Hydrodynamics. <i>Electronic Journal of Probability</i>.  Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/20-EJP536\">https://doi.org/10.1214/20-EJP536</a>","short":"F. Redig, E. Saada, F. Sau, Electronic Journal of Probability 25 (2020).","ista":"Redig F, Saada E, Sau F. 2020. Symmetric simple exclusion process in dynamic environment: Hydrodynamics. Electronic Journal of Probability. 25, 138.","ama":"Redig F, Saada E, Sau F. Symmetric simple exclusion process in dynamic environment: Hydrodynamics. <i>Electronic Journal of Probability</i>. 2020;25. doi:<a href=\"https://doi.org/10.1214/20-EJP536\">10.1214/20-EJP536</a>","mla":"Redig, Frank, et al. “Symmetric Simple Exclusion Process in Dynamic Environment: Hydrodynamics.” <i>Electronic Journal of Probability</i>, vol. 25, 138,  Institute of Mathematical Statistics, 2020, doi:<a href=\"https://doi.org/10.1214/20-EJP536\">10.1214/20-EJP536</a>."},"publication_status":"published","ddc":["510"],"article_number":"138","isi":1,"external_id":{"isi":["000591737500001"],"arxiv":["1811.01366"]},"title":"Symmetric simple exclusion process in dynamic environment: Hydrodynamics","doi":"10.1214/20-EJP536","year":"2020","ec_funded":1},{"external_id":{"isi":["000546975100017"],"arxiv":["1809.01092"]},"title":"Scaling limits of discrete optimal transport","doi":"10.1137/19M1243440","year":"2020","isi":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1809.01092"}],"author":[{"full_name":"Gladbach, Peter","last_name":"Gladbach","first_name":"Peter"},{"last_name":"Kopfer","full_name":"Kopfer, Eva","first_name":"Eva"},{"full_name":"Maas, Jan","last_name":"Maas","orcid":"0000-0002-0845-1338","first_name":"Jan","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87"}],"abstract":[{"lang":"eng","text":"We consider dynamical transport metrics for probability measures on discretisations of a bounded convex domain in ℝd. These metrics are natural discrete counterparts to the Kantorovich metric 𝕎2, defined using a Benamou-Brenier type formula. Under mild assumptions we prove an asymptotic upper bound for the discrete transport metric Wt in terms of 𝕎2, as the size of the mesh T tends to 0. However, we show that the corresponding lower bound may fail in general, even on certain one-dimensional and symmetric two-dimensional meshes. In addition, we show that the asymptotic lower bound holds under an isotropy assumption on the mesh, which turns out to be essentially necessary. This assumption is satisfied, e.g., for tilings by convex regular polygons, and it implies Gromov-Hausdorff convergence of the transport metric."}],"citation":{"ieee":"P. Gladbach, E. Kopfer, and J. Maas, “Scaling limits of discrete optimal transport,” <i>SIAM Journal on Mathematical Analysis</i>, vol. 52, no. 3. Society for Industrial and Applied Mathematics, pp. 2759–2802, 2020.","apa":"Gladbach, P., Kopfer, E., &#38; Maas, J. (2020). Scaling limits of discrete optimal transport. <i>SIAM Journal on Mathematical Analysis</i>. Society for Industrial and Applied Mathematics. <a href=\"https://doi.org/10.1137/19M1243440\">https://doi.org/10.1137/19M1243440</a>","chicago":"Gladbach, Peter, Eva Kopfer, and Jan Maas. “Scaling Limits of Discrete Optimal Transport.” <i>SIAM Journal on Mathematical Analysis</i>. Society for Industrial and Applied Mathematics, 2020. <a href=\"https://doi.org/10.1137/19M1243440\">https://doi.org/10.1137/19M1243440</a>.","mla":"Gladbach, Peter, et al. “Scaling Limits of Discrete Optimal Transport.” <i>SIAM Journal on Mathematical Analysis</i>, vol. 52, no. 3, Society for Industrial and Applied Mathematics, 2020, pp. 2759–802, doi:<a href=\"https://doi.org/10.1137/19M1243440\">10.1137/19M1243440</a>.","ama":"Gladbach P, Kopfer E, Maas J. Scaling limits of discrete optimal transport. <i>SIAM Journal on Mathematical Analysis</i>. 2020;52(3):2759-2802. doi:<a href=\"https://doi.org/10.1137/19M1243440\">10.1137/19M1243440</a>","short":"P. Gladbach, E. Kopfer, J. Maas, SIAM Journal on Mathematical Analysis 52 (2020) 2759–2802.","ista":"Gladbach P, Kopfer E, Maas J. 2020. Scaling limits of discrete optimal transport. SIAM Journal on Mathematical Analysis. 52(3), 2759–2802."},"publication_status":"published","oa_version":"Preprint","quality_controlled":"1","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","publication_identifier":{"eissn":["10957154"],"issn":["00361410"]},"_id":"71","article_processing_charge":"No","oa":1,"date_updated":"2023-09-18T08:13:15Z","publist_id":"7983","volume":52,"arxiv":1,"language":[{"iso":"eng"}],"scopus_import":"1","publisher":"Society for Industrial and Applied Mathematics","date_published":"2020-10-01T00:00:00Z","article_type":"original","month":"10","date_created":"2018-12-11T11:44:28Z","department":[{"_id":"JaMa"}],"status":"public","intvolume":"        52","type":"journal_article","day":"01","page":"2759-2802","publication":"SIAM Journal on Mathematical Analysis","issue":"3"},{"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1902.07635"}],"isi":1,"external_id":{"isi":["000531049800007"],"arxiv":["1902.07635"]},"title":"Nondivergence form quasilinear heat equations driven by space-time white noise","doi":"10.1016/j.anihpc.2020.01.003","year":"2020","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa_version":"Preprint","quality_controlled":"1","_id":"7388","publication_identifier":{"issn":["0294-1449"]},"date_updated":"2023-08-17T14:35:46Z","volume":37,"oa":1,"article_processing_charge":"No","arxiv":1,"author":[{"id":"44ECEDF2-F248-11E8-B48F-1D18A9856A87","last_name":"Gerencser","full_name":"Gerencser, Mate","first_name":"Mate"}],"abstract":[{"lang":"eng","text":"We give a Wong-Zakai type characterisation of the solutions of quasilinear heat equations driven by space-time white noise in 1 + 1 dimensions. In order to show that the renormalisation counterterms are local in the solution, a careful arrangement of a few hundred terms is required. The main tool in this computation is a general ‘integration by parts’ formula that provides a number of linear identities for the renormalisation constants."}],"publication_status":"published","citation":{"chicago":"Gerencser, Mate. “Nondivergence Form Quasilinear Heat Equations Driven by Space-Time White Noise.” <i>Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire</i>. Elsevier, 2020. <a href=\"https://doi.org/10.1016/j.anihpc.2020.01.003\">https://doi.org/10.1016/j.anihpc.2020.01.003</a>.","apa":"Gerencser, M. (2020). Nondivergence form quasilinear heat equations driven by space-time white noise. <i>Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.anihpc.2020.01.003\">https://doi.org/10.1016/j.anihpc.2020.01.003</a>","ieee":"M. Gerencser, “Nondivergence form quasilinear heat equations driven by space-time white noise,” <i>Annales de l’Institut Henri Poincaré C, Analyse non linéaire</i>, vol. 37, no. 3. Elsevier, pp. 663–682, 2020.","ista":"Gerencser M. 2020. Nondivergence form quasilinear heat equations driven by space-time white noise. Annales de l’Institut Henri Poincaré C, Analyse non linéaire. 37(3), 663–682.","short":"M. Gerencser, Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire 37 (2020) 663–682.","mla":"Gerencser, Mate. “Nondivergence Form Quasilinear Heat Equations Driven by Space-Time White Noise.” <i>Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire</i>, vol. 37, no. 3, Elsevier, 2020, pp. 663–82, doi:<a href=\"https://doi.org/10.1016/j.anihpc.2020.01.003\">10.1016/j.anihpc.2020.01.003</a>.","ama":"Gerencser M. Nondivergence form quasilinear heat equations driven by space-time white noise. <i>Annales de l’Institut Henri Poincaré C, Analyse non linéaire</i>. 2020;37(3):663-682. doi:<a href=\"https://doi.org/10.1016/j.anihpc.2020.01.003\">10.1016/j.anihpc.2020.01.003</a>"},"date_created":"2020-01-29T09:39:41Z","department":[{"_id":"JaMa"}],"language":[{"iso":"eng"}],"publisher":"Elsevier","scopus_import":"1","date_published":"2020-05-01T00:00:00Z","article_type":"original","month":"05","page":"663-682","issue":"3","publication":"Annales de l'Institut Henri Poincaré C, Analyse non linéaire","status":"public","intvolume":"        37","type":"journal_article","day":"01"},{"year":"2020","doi":"10.1007/978-3-030-36020-7_1","ec_funded":1,"external_id":{"isi":["000557689300003"],"arxiv":["1808.07350"]},"title":"Gromov's waist of non-radial Gaussian measures and radial non-Gaussian measures","main_file_link":[{"url":"https://arxiv.org/abs/1808.07350","open_access":"1"}],"isi":1,"citation":{"ieee":"A. Akopyan and R. Karasev, “Gromov’s waist of non-radial Gaussian measures and radial non-Gaussian measures,” in <i>Geometric Aspects of Functional Analysis</i>, vol. 2256, B. Klartag and E. Milman, Eds. Springer Nature, 2020, pp. 1–27.","apa":"Akopyan, A., &#38; Karasev, R. (2020). Gromov’s waist of non-radial Gaussian measures and radial non-Gaussian measures. In B. Klartag &#38; E. Milman (Eds.), <i>Geometric Aspects of Functional Analysis</i> (Vol. 2256, pp. 1–27). Springer Nature. <a href=\"https://doi.org/10.1007/978-3-030-36020-7_1\">https://doi.org/10.1007/978-3-030-36020-7_1</a>","chicago":"Akopyan, Arseniy, and Roman Karasev. “Gromov’s Waist of Non-Radial Gaussian Measures and Radial Non-Gaussian Measures.” In <i>Geometric Aspects of Functional Analysis</i>, edited by Bo’az Klartag and Emanuel Milman, 2256:1–27. LNM. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/978-3-030-36020-7_1\">https://doi.org/10.1007/978-3-030-36020-7_1</a>.","mla":"Akopyan, Arseniy, and Roman Karasev. “Gromov’s Waist of Non-Radial Gaussian Measures and Radial Non-Gaussian Measures.” <i>Geometric Aspects of Functional Analysis</i>, edited by Bo’az Klartag and Emanuel Milman, vol. 2256, Springer Nature, 2020, pp. 1–27, doi:<a href=\"https://doi.org/10.1007/978-3-030-36020-7_1\">10.1007/978-3-030-36020-7_1</a>.","ama":"Akopyan A, Karasev R. Gromov’s waist of non-radial Gaussian measures and radial non-Gaussian measures. In: Klartag B, Milman E, eds. <i>Geometric Aspects of Functional Analysis</i>. Vol 2256. LNM. Springer Nature; 2020:1-27. doi:<a href=\"https://doi.org/10.1007/978-3-030-36020-7_1\">10.1007/978-3-030-36020-7_1</a>","short":"A. Akopyan, R. Karasev, in:, B. Klartag, E. Milman (Eds.), Geometric Aspects of Functional Analysis, Springer Nature, 2020, pp. 1–27.","ista":"Akopyan A, Karasev R. 2020.Gromov’s waist of non-radial Gaussian measures and radial non-Gaussian measures. In: Geometric Aspects of Functional Analysis. vol. 2256, 1–27."},"publication_status":"published","abstract":[{"text":"We study the Gromov waist in the sense of t-neighborhoods for measures in the Euclidean  space,  motivated  by  the  famous  theorem  of  Gromov  about  the  waist  of  radially symmetric Gaussian measures.  In particular, it turns our possible to extend Gromov’s original result  to  the  case  of  not  necessarily  radially  symmetric  Gaussian  measure.   We  also  provide examples of measures having no t-neighborhood waist property, including a rather wide class\r\nof compactly supported radially symmetric measures and their maps into the Euclidean space of dimension at least 2.\r\nWe  use  a  simpler  form  of  Gromov’s  pancake  argument  to  produce  some  estimates  of t-neighborhoods of (weighted) volume-critical submanifolds in the spirit of the waist theorems, including neighborhoods of algebraic manifolds in the complex projective space. In the appendix of this paper we provide for reader’s convenience a more detailed explanation of the Caffarelli theorem that we use to handle not necessarily radially symmetric Gaussian\r\nmeasures.","lang":"eng"}],"author":[{"last_name":"Akopyan","full_name":"Akopyan, Arseniy","orcid":"0000-0002-2548-617X","first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Karasev, Roman","last_name":"Karasev","first_name":"Roman"}],"editor":[{"first_name":"Bo'az","full_name":"Klartag, Bo'az","last_name":"Klartag"},{"first_name":"Emanuel","last_name":"Milman","full_name":"Milman, Emanuel"}],"arxiv":1,"article_processing_charge":"No","volume":2256,"date_updated":"2023-08-17T13:48:31Z","oa":1,"publication_identifier":{"issn":["00758434"],"eisbn":["9783030360207"],"isbn":["9783030360191"],"eissn":["16179692"]},"_id":"74","project":[{"grant_number":"716117","call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425","name":"Optimal Transport and Stochastic Dynamics"}],"oa_version":"Preprint","quality_controlled":"1","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","month":"06","date_published":"2020-06-21T00:00:00Z","scopus_import":"1","publisher":"Springer Nature","language":[{"iso":"eng"}],"department":[{"_id":"HeEd"},{"_id":"JaMa"}],"date_created":"2018-12-11T11:44:29Z","day":"21","series_title":"LNM","type":"book_chapter","intvolume":"      2256","status":"public","publication":"Geometric Aspects of Functional Analysis","page":"1-27"},{"date_created":"2020-02-23T21:43:50Z","department":[{"_id":"JaMa"}],"publisher":"Elsevier","language":[{"iso":"eng"}],"month":"05","date_published":"2020-05-13T00:00:00Z","article_type":"original","publication":"Advances in Mathematics","intvolume":"       365","status":"public","day":"13","type":"journal_article","ddc":["515"],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1811.01205"}],"article_number":"107053","isi":1,"title":"From Wigner-Yanase-Dyson conjecture to Carlen-Frank-Lieb conjecture","external_id":{"arxiv":["1811.01205"],"isi":["000522798000001"]},"year":"2020","doi":"10.1016/j.aim.2020.107053","ec_funded":1,"_id":"7509","quality_controlled":"1","oa_version":"Preprint","project":[{"call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","acknowledgement":"The author would like to thank Quanhua Xu, Adam Skalski, Ke Li and Zhi Yin for their valuable comments. He also would like to thank the anonymous referees for pointing out some errors in an earlier version of this paper and for helpful comments and suggestions that make this paper better. The research was partially supported by the NCN (National Centre of Science) grant 2014/14/E/ST1/00525, the French project ISITE-BFC (contract ANR-15-IDEX-03), NSFC No. 11826012, and the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 754411.","arxiv":1,"article_processing_charge":"No","oa":1,"volume":365,"date_updated":"2023-08-18T06:37:09Z","abstract":[{"lang":"eng","text":"In this paper we study the joint convexity/concavity of the trace functions Ψp,q,s(A,B)=Tr(Bq2K∗ApKBq2)s,  p,q,s∈R,\r\nwhere A and B are positive definite matrices and K is any fixed invertible matrix. We will give full range of (p,q,s)∈R3 for Ψp,q,s to be jointly convex/concave for all K. As a consequence, we confirm a conjecture of Carlen, Frank and Lieb. In particular, we confirm a weaker conjecture of Audenaert and Datta and obtain the full range of (α,z) for α-z Rényi relative entropies to be monotone under completely positive trace preserving maps. We also give simpler proofs of many known results, including the concavity of Ψp,0,1/p for 0<p<1 which was first proved by Epstein using complex analysis. The key is to reduce the problem to the joint convexity/concavity of the trace functions Ψp,1−p,1(A,B)=TrK∗ApKB1−p,  −1≤p≤1, using a variational method. "}],"author":[{"first_name":"Haonan","full_name":"Zhang, Haonan","last_name":"Zhang","id":"D8F41E38-9E66-11E9-A9E2-65C2E5697425"}],"citation":{"chicago":"Zhang, Haonan. “From Wigner-Yanase-Dyson Conjecture to Carlen-Frank-Lieb Conjecture.” <i>Advances in Mathematics</i>. Elsevier, 2020. <a href=\"https://doi.org/10.1016/j.aim.2020.107053\">https://doi.org/10.1016/j.aim.2020.107053</a>.","ieee":"H. Zhang, “From Wigner-Yanase-Dyson conjecture to Carlen-Frank-Lieb conjecture,” <i>Advances in Mathematics</i>, vol. 365. Elsevier, 2020.","apa":"Zhang, H. (2020). From Wigner-Yanase-Dyson conjecture to Carlen-Frank-Lieb conjecture. <i>Advances in Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.aim.2020.107053\">https://doi.org/10.1016/j.aim.2020.107053</a>","ista":"Zhang H. 2020. From Wigner-Yanase-Dyson conjecture to Carlen-Frank-Lieb conjecture. Advances in Mathematics. 365, 107053.","short":"H. Zhang, Advances in Mathematics 365 (2020).","ama":"Zhang H. From Wigner-Yanase-Dyson conjecture to Carlen-Frank-Lieb conjecture. <i>Advances in Mathematics</i>. 2020;365. doi:<a href=\"https://doi.org/10.1016/j.aim.2020.107053\">10.1016/j.aim.2020.107053</a>","mla":"Zhang, Haonan. “From Wigner-Yanase-Dyson Conjecture to Carlen-Frank-Lieb Conjecture.” <i>Advances in Mathematics</i>, vol. 365, 107053, Elsevier, 2020, doi:<a href=\"https://doi.org/10.1016/j.aim.2020.107053\">10.1016/j.aim.2020.107053</a>."},"publication_status":"published"}]