[{"quality_controlled":"1","abstract":[{"text":"Empirical essays of fitness landscapes suggest that they may be rugged, that is having multiple fitness peaks. Such fitness landscapes, those that have multiple peaks, necessarily have special local structures, called reciprocal sign epistasis (Poelwijk et al. in J Theor Biol 272:141–144, 2011). Here, we investigate the quantitative relationship between the number of fitness peaks and the number of reciprocal sign epistatic interactions. Previously, it has been shown (Poelwijk et al. in J Theor Biol 272:141–144, 2011) that pairwise reciprocal sign epistasis is a necessary but not sufficient condition for the existence of multiple peaks. Applying discrete Morse theory, which to our knowledge has never been used in this context, we extend this result by giving the minimal number of reciprocal sign epistatic interactions required to create a given number of peaks.","lang":"eng"}],"publication_status":"published","has_accepted_license":"1","status":"public","language":[{"iso":"eng"}],"ddc":["510","570"],"article_type":"original","file":[{"file_name":"2022_BulletinMathBiology_Saona.pdf","success":1,"access_level":"open_access","checksum":"05a1fe7d10914a00c2bca9b447993a65","relation":"main_file","date_updated":"2022-06-20T07:51:32Z","content_type":"application/pdf","file_size":463025,"date_created":"2022-06-20T07:51:32Z","creator":"dernst","file_id":"11455"}],"citation":{"ieee":"R. J. Saona Urmeneta, F. Kondrashov, and K. Khudiakova, “Relation between the number of peaks and the number of reciprocal sign epistatic interactions,” <i>Bulletin of Mathematical Biology</i>, vol. 84, no. 8. Springer Nature, 2022.","apa":"Saona Urmeneta, R. J., Kondrashov, F., &#38; Khudiakova, K. (2022). Relation between the number of peaks and the number of reciprocal sign epistatic interactions. <i>Bulletin of Mathematical Biology</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s11538-022-01029-z\">https://doi.org/10.1007/s11538-022-01029-z</a>","short":"R.J. Saona Urmeneta, F. Kondrashov, K. Khudiakova, Bulletin of Mathematical Biology 84 (2022).","mla":"Saona Urmeneta, Raimundo J., et al. “Relation between the Number of Peaks and the Number of Reciprocal Sign Epistatic Interactions.” <i>Bulletin of Mathematical Biology</i>, vol. 84, no. 8, 74, Springer Nature, 2022, doi:<a href=\"https://doi.org/10.1007/s11538-022-01029-z\">10.1007/s11538-022-01029-z</a>.","ista":"Saona Urmeneta RJ, Kondrashov F, Khudiakova K. 2022. Relation between the number of peaks and the number of reciprocal sign epistatic interactions. Bulletin of Mathematical Biology. 84(8), 74.","ama":"Saona Urmeneta RJ, Kondrashov F, Khudiakova K. Relation between the number of peaks and the number of reciprocal sign epistatic interactions. <i>Bulletin of Mathematical Biology</i>. 2022;84(8). doi:<a href=\"https://doi.org/10.1007/s11538-022-01029-z\">10.1007/s11538-022-01029-z</a>","chicago":"Saona Urmeneta, Raimundo J, Fyodor Kondrashov, and Kseniia Khudiakova. “Relation between the Number of Peaks and the Number of Reciprocal Sign Epistatic Interactions.” <i>Bulletin of Mathematical Biology</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s11538-022-01029-z\">https://doi.org/10.1007/s11538-022-01029-z</a>."},"type":"journal_article","year":"2022","author":[{"last_name":"Saona Urmeneta","orcid":"0000-0001-5103-038X","full_name":"Saona Urmeneta, Raimundo J","first_name":"Raimundo J","id":"BD1DF4C4-D767-11E9-B658-BC13E6697425"},{"id":"44FDEF62-F248-11E8-B48F-1D18A9856A87","first_name":"Fyodor","full_name":"Kondrashov, Fyodor","orcid":"0000-0001-8243-4694","last_name":"Kondrashov"},{"full_name":"Khudiakova, Kseniia","orcid":"0000-0002-6246-1465","last_name":"Khudiakova","first_name":"Kseniia","id":"4E6DC800-AE37-11E9-AC72-31CAE5697425"}],"isi":1,"department":[{"_id":"GradSch"},{"_id":"NiBa"},{"_id":"JaMa"}],"publication_identifier":{"eissn":["1522-9602"],"issn":["0092-8240"]},"tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"publisher":"Springer Nature","day":"17","doi":"10.1007/s11538-022-01029-z","oa_version":"Published Version","article_number":"74","oa":1,"intvolume":"        84","acknowledgement":"We are grateful to Herbert Edelsbrunner and Jeferson Zapata for helpful discussions. Open access funding provided by Austrian Science Fund (FWF). Partially supported by the ERC Consolidator (771209–CharFL) and the FWF Austrian Science Fund (I5127-B) grants to FAK.","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","issue":"8","related_material":{"link":[{"relation":"erratum","url":"https://doi.org/10.1007/s11538-022-01118-z"}]},"volume":84,"scopus_import":"1","article_processing_charge":"Yes (via OA deal)","keyword":["Computational Theory and Mathematics","General Agricultural and Biological Sciences","Pharmacology","General Environmental Science","General Biochemistry","Genetics and Molecular Biology","General Mathematics","Immunology","General Neuroscience"],"date_published":"2022-06-17T00:00:00Z","ec_funded":1,"title":"Relation between the number of peaks and the number of reciprocal sign epistatic interactions","date_updated":"2023-08-03T07:20:53Z","month":"06","_id":"11447","project":[{"call_identifier":"H2020","grant_number":"771209","_id":"26580278-B435-11E9-9278-68D0E5697425","name":"Characterizing the fitness landscape on population and global scales"},{"name":"Evolutionary analysis of gene regulation","grant_number":"I05127","_id":"c098eddd-5a5b-11eb-8a69-abe27170a68f"}],"external_id":{"isi":["000812509800001"]},"date_created":"2022-06-17T16:16:15Z","publication":"Bulletin of Mathematical Biology","file_date_updated":"2022-06-20T07:51:32Z"},{"quality_controlled":"1","status":"public","language":[{"iso":"eng"}],"publication_status":"published","abstract":[{"text":"This paper contains two contributions in the study of optimal transport on metric graphs. Firstly, we prove a Benamou–Brenier formula for the Wasserstein distance, which establishes the equivalence of static and dynamical optimal transport. Secondly, in the spirit of Jordan–Kinderlehrer–Otto, we show that McKean–Vlasov equations can be formulated as gradient flow of the free energy in the Wasserstein space of probability measures. The proofs of these results are based on careful regularisation arguments to circumvent some of the difficulties arising in metric graphs, namely, branching of geodesics and the failure of semi-convexity of entropy functionals in the Wasserstein space.","lang":"eng"}],"article_type":"original","type":"journal_article","citation":{"ieee":"M. Erbar, D. L. Forkert, J. Maas, and D. Mugnolo, “Gradient flow formulation of diffusion equations in the Wasserstein space over a metric graph,” <i>Networks and Heterogeneous Media</i>, vol. 17, no. 5. American Institute of Mathematical Sciences, pp. 687–717, 2022.","short":"M. Erbar, D.L. Forkert, J. Maas, D. Mugnolo, Networks and Heterogeneous Media 17 (2022) 687–717.","apa":"Erbar, M., Forkert, D. L., Maas, J., &#38; Mugnolo, D. (2022). Gradient flow formulation of diffusion equations in the Wasserstein space over a metric graph. <i>Networks and Heterogeneous Media</i>. American Institute of Mathematical Sciences. <a href=\"https://doi.org/10.3934/nhm.2022023\">https://doi.org/10.3934/nhm.2022023</a>","mla":"Erbar, Matthias, et al. “Gradient Flow Formulation of Diffusion Equations in the Wasserstein Space over a Metric Graph.” <i>Networks and Heterogeneous Media</i>, vol. 17, no. 5, American Institute of Mathematical Sciences, 2022, pp. 687–717, doi:<a href=\"https://doi.org/10.3934/nhm.2022023\">10.3934/nhm.2022023</a>.","ista":"Erbar M, Forkert DL, Maas J, Mugnolo D. 2022. Gradient flow formulation of diffusion equations in the Wasserstein space over a metric graph. Networks and Heterogeneous Media. 17(5), 687–717.","ama":"Erbar M, Forkert DL, Maas J, Mugnolo D. Gradient flow formulation of diffusion equations in the Wasserstein space over a metric graph. <i>Networks and Heterogeneous Media</i>. 2022;17(5):687-717. doi:<a href=\"https://doi.org/10.3934/nhm.2022023\">10.3934/nhm.2022023</a>","chicago":"Erbar, Matthias, Dominik L Forkert, Jan Maas, and Delio Mugnolo. “Gradient Flow Formulation of Diffusion Equations in the Wasserstein Space over a Metric Graph.” <i>Networks and Heterogeneous Media</i>. American Institute of Mathematical Sciences, 2022. <a href=\"https://doi.org/10.3934/nhm.2022023\">https://doi.org/10.3934/nhm.2022023</a>."},"year":"2022","author":[{"first_name":"Matthias","last_name":"Erbar","full_name":"Erbar, Matthias"},{"full_name":"Forkert, Dominik L","last_name":"Forkert","first_name":"Dominik L","id":"35C79D68-F248-11E8-B48F-1D18A9856A87"},{"id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","first_name":"Jan","full_name":"Maas, Jan","orcid":"0000-0002-0845-1338","last_name":"Maas"},{"first_name":"Delio","last_name":"Mugnolo","full_name":"Mugnolo, Delio"}],"isi":1,"publication_identifier":{"issn":["1556-1801"],"eissn":["1556-181X"]},"department":[{"_id":"JaMa"}],"day":"01","publisher":"American Institute of Mathematical Sciences","oa_version":"Preprint","arxiv":1,"doi":"10.3934/nhm.2022023","oa":1,"intvolume":"        17","issue":"5","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","acknowledgement":"ME acknowledges funding by the Deutsche Forschungsgemeinschaft (DFG), Grant SFB 1283/2 2021 – 317210226. DF and JM were supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 716117). JM also acknowledges support by the Austrian Science Fund (FWF), Project SFB F65. The work of DM was partially supported by the Deutsche Forschungsgemeinschaft\r\n(DFG), Grant 397230547. This article is based upon work from COST Action\r\n18232 MAT-DYN-NET, supported by COST (European Cooperation in Science\r\nand Technology), www.cost.eu. We wish to thank Martin Burger and Jan-Frederik\r\nPietschmann for useful discussions. We are grateful to the anonymous referees for\r\ntheir careful reading and useful suggestions.","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2105.05677"}],"volume":17,"scopus_import":"1","ec_funded":1,"article_processing_charge":"No","date_published":"2022-10-01T00:00:00Z","month":"10","date_updated":"2023-08-03T12:25:49Z","title":"Gradient flow formulation of diffusion equations in the Wasserstein space over a metric graph","external_id":{"isi":["000812422100001"],"arxiv":["2105.05677"]},"date_created":"2022-07-31T22:01:46Z","project":[{"name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems"}],"_id":"11700","page":"687-717","publication":"Networks and Heterogeneous Media"},{"publication_status":"published","abstract":[{"text":"We consider finite-volume approximations of Fokker--Planck equations on bounded convex domains in $\\mathbb{R}^d$ and study the corresponding gradient flow structures. We reprove the convergence of the discrete to continuous Fokker--Planck equation via the method of evolutionary $\\Gamma$-convergence, i.e., we pass to the limit at the level of the gradient flow structures, generalizing the one-dimensional result obtained by Disser and Liero. The proof is of variational nature and relies on a Mosco convergence result for functionals in the discrete-to-continuum limit that is of independent interest. Our results apply to arbitrary regular meshes, even though the associated discrete transport distances may fail to converge to the Wasserstein distance in this generality.","lang":"eng"}],"language":[{"iso":"eng"}],"status":"public","quality_controlled":"1","type":"journal_article","citation":{"ista":"Forkert DL, Maas J, Portinale L. 2022. Evolutionary $\\Gamma$-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions. SIAM Journal on Mathematical Analysis. 54(4), 4297–4333.","mla":"Forkert, Dominik L., et al. “Evolutionary $\\Gamma$-Convergence of Entropic Gradient Flow Structures for Fokker-Planck Equations in Multiple Dimensions.” <i>SIAM Journal on Mathematical Analysis</i>, vol. 54, no. 4, Society for Industrial and Applied Mathematics, 2022, pp. 4297–333, doi:<a href=\"https://doi.org/10.1137/21M1410968\">10.1137/21M1410968</a>.","chicago":"Forkert, Dominik L, Jan Maas, and Lorenzo Portinale. “Evolutionary $\\Gamma$-Convergence of Entropic Gradient Flow Structures for Fokker-Planck Equations in Multiple Dimensions.” <i>SIAM Journal on Mathematical Analysis</i>. Society for Industrial and Applied Mathematics, 2022. <a href=\"https://doi.org/10.1137/21M1410968\">https://doi.org/10.1137/21M1410968</a>.","ama":"Forkert DL, Maas J, Portinale L. Evolutionary $\\Gamma$-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions. <i>SIAM Journal on Mathematical Analysis</i>. 2022;54(4):4297-4333. doi:<a href=\"https://doi.org/10.1137/21M1410968\">10.1137/21M1410968</a>","ieee":"D. L. Forkert, J. Maas, and L. Portinale, “Evolutionary $\\Gamma$-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions,” <i>SIAM Journal on Mathematical Analysis</i>, vol. 54, no. 4. Society for Industrial and Applied Mathematics, pp. 4297–4333, 2022.","short":"D.L. Forkert, J. Maas, L. Portinale, SIAM Journal on Mathematical Analysis 54 (2022) 4297–4333.","apa":"Forkert, D. L., Maas, J., &#38; Portinale, L. (2022). Evolutionary $\\Gamma$-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions. <i>SIAM Journal on Mathematical Analysis</i>. Society for Industrial and Applied Mathematics. <a href=\"https://doi.org/10.1137/21M1410968\">https://doi.org/10.1137/21M1410968</a>"},"article_type":"original","department":[{"_id":"JaMa"}],"publication_identifier":{"issn":["0036-1410"],"eissn":["1095-7154"]},"author":[{"last_name":"Forkert","full_name":"Forkert, Dominik L","id":"35C79D68-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik L"},{"first_name":"Jan","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-0845-1338","full_name":"Maas, Jan","last_name":"Maas"},{"full_name":"Portinale, Lorenzo","last_name":"Portinale","id":"30AD2CBC-F248-11E8-B48F-1D18A9856A87","first_name":"Lorenzo"}],"isi":1,"year":"2022","doi":"10.1137/21M1410968","arxiv":1,"oa_version":"Preprint","publisher":"Society for Industrial and Applied Mathematics","day":"18","volume":54,"main_file_link":[{"open_access":"1","url":" https://doi.org/10.48550/arXiv.2008.10962"}],"related_material":{"record":[{"status":"public","relation":"earlier_version","id":"10022"}]},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","issue":"4","acknowledgement":"This work was supported by the European Research Council (ERC) under the European Union's Horizon 2020 Research and Innovation Programme grant 716117 and by the AustrianScience Fund (FWF) through grants F65 and W1245.","intvolume":"        54","oa":1,"scopus_import":"1","date_updated":"2023-08-03T12:37:21Z","title":"Evolutionary $\\Gamma$-convergence of entropic gradient flow structures for Fokker-Planck equations in multiple dimensions","month":"07","date_published":"2022-07-18T00:00:00Z","article_processing_charge":"No","keyword":["Fokker--Planck equation","gradient flow","evolutionary $\\Gamma$-convergence"],"ec_funded":1,"publication":"SIAM Journal on Mathematical Analysis","page":"4297-4333","_id":"11739","project":[{"call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics"},{"name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"},{"name":"Dissipation and Dispersion in Nonlinear Partial Differential Equations","_id":"260788DE-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"date_created":"2022-08-07T22:01:59Z","external_id":{"isi":["000889274600001"],"arxiv":["2008.10962"]}},{"tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"department":[{"_id":"JaMa"}],"publication_identifier":{"eissn":["2538-225X"]},"author":[{"full_name":"Wirth, Melchior","orcid":"0000-0002-0519-4241","last_name":"Wirth","first_name":"Melchior","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E"}],"year":"2022","oa_version":"Published Version","doi":"10.1007/s43036-022-00199-w","day":"01","publisher":"Springer Nature","language":[{"iso":"eng"}],"has_accepted_license":"1","status":"public","publication_status":"published","abstract":[{"text":"A domain is called Kac regular for a quadratic form on L2 if every functions vanishing almost everywhere outside the domain can be approximated in form norm by functions with compact support in the domain. It is shown that this notion is stable under domination of quadratic forms. As applications measure perturbations of quasi-regular Dirichlet forms, Cheeger energies on metric measure spaces and Schrödinger operators on manifolds are studied. Along the way a characterization of the Sobolev space with Dirichlet boundary conditions on domains in infinitesimally Riemannian metric measure spaces is obtained.","lang":"eng"}],"quality_controlled":"1","citation":{"ama":"Wirth M. Kac regularity and domination of quadratic forms. <i>Advances in Operator Theory</i>. 2022;7(3). doi:<a href=\"https://doi.org/10.1007/s43036-022-00199-w\">10.1007/s43036-022-00199-w</a>","chicago":"Wirth, Melchior. “Kac Regularity and Domination of Quadratic Forms.” <i>Advances in Operator Theory</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s43036-022-00199-w\">https://doi.org/10.1007/s43036-022-00199-w</a>.","mla":"Wirth, Melchior. “Kac Regularity and Domination of Quadratic Forms.” <i>Advances in Operator Theory</i>, vol. 7, no. 3, 38, Springer Nature, 2022, doi:<a href=\"https://doi.org/10.1007/s43036-022-00199-w\">10.1007/s43036-022-00199-w</a>.","ista":"Wirth M. 2022. Kac regularity and domination of quadratic forms. Advances in Operator Theory. 7(3), 38.","apa":"Wirth, M. (2022). Kac regularity and domination of quadratic forms. <i>Advances in Operator Theory</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s43036-022-00199-w\">https://doi.org/10.1007/s43036-022-00199-w</a>","short":"M. Wirth, Advances in Operator Theory 7 (2022).","ieee":"M. Wirth, “Kac regularity and domination of quadratic forms,” <i>Advances in Operator Theory</i>, vol. 7, no. 3. Springer Nature, 2022."},"type":"journal_article","file":[{"creator":"dernst","date_created":"2022-08-18T08:02:34Z","file_id":"11921","file_name":"2022_AdvancesOperatorTheory_Wirth.pdf","access_level":"open_access","success":1,"checksum":"913474844a1b38264fb710746d5e2e98","relation":"main_file","file_size":389060,"content_type":"application/pdf","date_updated":"2022-08-18T08:02:34Z"}],"article_type":"original","ddc":["510"],"month":"07","title":"Kac regularity and domination of quadratic forms","date_updated":"2023-02-21T10:08:07Z","date_published":"2022-07-01T00:00:00Z","article_processing_charge":"Yes (via OA deal)","keyword":["Algebra and Number Theory","Analysis"],"file_date_updated":"2022-08-18T08:02:34Z","publication":"Advances in Operator Theory","date_created":"2022-08-18T07:22:24Z","_id":"11916","volume":7,"issue":"3","acknowledgement":"The author was supported by the German Academic Scholarship Foundation (Studienstiftung des deutschen Volkes) and by the German Research Foundation (DFG) via RTG 1523/2. The author would like to thank Daniel Lenz for his support and encouragement during the author’s ongoing graduate studies and him as well as Marcel Schmidt for fruitful discussions on domination of quadratic forms. He wants to thank Batu Güneysu and Peter Stollmann for valuable comments on a preliminary version of this article. He would also like to thank the organizers of the conference Analysis and Geometry on Graphs and Manifolds in Potsdam, where the initial motivation of this article was conceived, and the organizers of the intense activity period Metric Measure Spaces and Ricci Curvature at MPIM in Bonn, where this work was finished.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria).","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":"         7","oa":1,"article_number":"38","scopus_import":"1"},{"intvolume":"        21","oa":1,"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","issue":"4","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.","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2005.14177"}],"volume":21,"_id":"10023","project":[{"call_identifier":"H2020","grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425","name":"Optimal Transport and Stochastic Dynamics"},{"grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems"}],"external_id":{"arxiv":["2005.14177"]},"date_created":"2021-09-19T08:53:19Z","publication":"Communications in Information and Systems","page":"481-536","keyword":["Markov Chain","relative entropy","time reversal","steepest descent","gradient flow"],"article_processing_charge":"No","date_published":"2021-06-04T00:00:00Z","ec_funded":1,"date_updated":"2021-09-20T12:51:18Z","title":"Trajectorial dissipation and gradient flow for the relative entropy in Markov chains","month":"06","article_type":"original","citation":{"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>","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>.","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.","apa":"Karatzas, I., Maas, J., &#38; Schachermayer, W. (2021). Trajectorial dissipation and gradient flow for the relative entropy in Markov chains. <i>Communications in Information and Systems</i>. International Press. <a href=\"https://doi.org/10.4310/CIS.2021.v21.n4.a1\">https://doi.org/10.4310/CIS.2021.v21.n4.a1</a>","ieee":"I. Karatzas, J. Maas, and W. Schachermayer, “Trajectorial dissipation and gradient flow for the relative entropy in Markov chains,” <i>Communications in Information and Systems</i>, vol. 21, no. 4. International Press, pp. 481–536, 2021."},"type":"journal_article","quality_controlled":"1","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"}],"publication_status":"published","status":"public","language":[{"iso":"eng"}],"publisher":"International Press","day":"04","doi":"10.4310/CIS.2021.v21.n4.a1","arxiv":1,"oa_version":"Preprint","year":"2021","author":[{"full_name":"Karatzas, Ioannis","last_name":"Karatzas","first_name":"Ioannis"},{"orcid":"0000-0002-0845-1338","full_name":"Maas, Jan","last_name":"Maas","first_name":"Jan","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Schachermayer, Walter","last_name":"Schachermayer","first_name":"Walter"}],"department":[{"_id":"JaMa"}],"publication_identifier":{"issn":["1526-7555"]}},{"doi":"10.1016/j.spa.2021.08.006","oa_version":"Published Version","arxiv":1,"publisher":"Elsevier","day":"27","department":[{"_id":"JaMa"}],"publication_identifier":{"issn":["0304-4149"]},"tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"isi":1,"author":[{"first_name":"Simone","last_name":"Floreani","full_name":"Floreani, Simone"},{"first_name":"Frank","full_name":"Redig, Frank","last_name":"Redig"},{"full_name":"Sau, Federico","last_name":"Sau","first_name":"Federico","id":"E1836206-9F16-11E9-8814-AEFDE5697425"}],"year":"2021","file":[{"file_name":"2021_StochasticProcessesAppl_Floreani.pdf","success":1,"access_level":"open_access","relation":"main_file","checksum":"56768c553d7218ee5714902ffec90ec4","date_updated":"2022-05-13T07:55:50Z","content_type":"application/pdf","file_size":2115791,"creator":"dernst","date_created":"2022-05-13T07:55:50Z","file_id":"11370"}],"citation":{"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.","short":"S. Floreani, F. Redig, F. Sau, Stochastic Processes and Their Applications 142 (2021) 124–158.","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>","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>.","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.","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>","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>."},"type":"journal_article","ddc":["519"],"article_type":"original","abstract":[{"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).","lang":"eng"}],"publication_status":"published","language":[{"iso":"eng"}],"has_accepted_license":"1","status":"public","quality_controlled":"1","file_date_updated":"2022-05-13T07:55:50Z","publication":"Stochastic Processes and their Applications","page":"124-158","project":[{"call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships"}],"_id":"10024","date_created":"2021-09-19T22:01:25Z","external_id":{"isi":["000697748500005"],"arxiv":["1911.12564"]},"title":"Hydrodynamics for the partial exclusion process in random environment","date_updated":"2023-08-14T06:52:43Z","month":"08","date_published":"2021-08-27T00:00:00Z","keyword":["hydrodynamic limit","random environment","random conductance model","arbitrary starting point quenched invariance principle","duality","mild solution"],"article_processing_charge":"Yes","ec_funded":1,"scopus_import":"1","volume":142,"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.","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","intvolume":"       142","oa":1},{"year":"2021","author":[{"last_name":"Portinale","full_name":"Portinale, Lorenzo","first_name":"Lorenzo","id":"30AD2CBC-F248-11E8-B48F-1D18A9856A87"}],"tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"publication_identifier":{"issn":["2663-337X"]},"department":[{"_id":"GradSch"},{"_id":"JaMa"}],"degree_awarded":"PhD","day":"22","publisher":"Institute of Science and Technology Austria","oa_version":"Published Version","doi":"10.15479/at:ista:10030","status":"public","has_accepted_license":"1","language":[{"iso":"eng"}],"publication_status":"published","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"}],"acknowledged_ssus":[{"_id":"M-Shop"},{"_id":"NanoFab"}],"ddc":["515"],"type":"dissertation","citation":{"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.","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>","short":"L. Portinale, Discrete-to-Continuum Limits of Transport Problems and Gradient Flows in the Space of Measures, Institute of Science and Technology Austria, 2021.","mla":"Portinale, Lorenzo. <i>Discrete-to-Continuum Limits of Transport Problems and Gradient Flows in the Space of Measures</i>. Institute of Science and Technology Austria, 2021, doi:<a href=\"https://doi.org/10.15479/at:ista:10030\">10.15479/at:ista:10030</a>.","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.","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>.","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>"},"file":[{"access_level":"closed","file_name":"tex_and_pictures.zip","date_updated":"2022-03-10T12:14:42Z","content_type":"application/x-zip-compressed","file_size":3876668,"relation":"source_file","checksum":"8cd60dcb8762e8f21867e21e8001e183","date_created":"2021-09-21T09:17:34Z","creator":"cchlebak","file_id":"10032"},{"date_updated":"2021-09-27T11:14:31Z","content_type":"application/pdf","file_size":2532673,"relation":"main_file","checksum":"9789e9d967c853c1503ec7f307170279","access_level":"open_access","file_name":"thesis_portinale_Final (1).pdf","file_id":"10047","creator":"cchlebak","date_created":"2021-09-27T11:14:31Z"}],"article_processing_charge":"No","date_published":"2021-09-22T00:00:00Z","month":"09","title":"Discrete-to-continuum limits of transport problems and gradient flows in the space of measures","date_updated":"2023-09-07T13:31:06Z","date_created":"2021-09-21T09:14:15Z","_id":"10030","project":[{"_id":"260788DE-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Dissipation and Dispersion in Nonlinear Partial Differential Equations"},{"name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"}],"supervisor":[{"first_name":"Jan","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","full_name":"Maas, Jan","orcid":"0000-0002-0845-1338","last_name":"Maas"}],"file_date_updated":"2022-03-10T12:14:42Z","oa":1,"acknowledgement":"The author gratefully acknowledges support by the Austrian Science Fund (FWF), grants No W1245.","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","related_material":{"record":[{"status":"public","relation":"part_of_dissertation","id":"10022"},{"id":"9792","status":"public","relation":"part_of_dissertation"},{"id":"7573","status":"public","relation":"part_of_dissertation"}]},"alternative_title":["ISTA Thesis"]},{"arxiv":1,"oa_version":"Preprint","doi":"10.1016/j.jfa.2021.109234","day":"15","publisher":"Elsevier","publication_identifier":{"eissn":["1096-0783"],"issn":["0022-1236"]},"department":[{"_id":"JaMa"}],"year":"2021","author":[{"last_name":"Dello Schiavo","orcid":"0000-0002-9881-6870","full_name":"Dello Schiavo, Lorenzo","first_name":"Lorenzo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E"},{"full_name":"Suzuki, Kohei","last_name":"Suzuki","first_name":"Kohei"}],"isi":1,"citation":{"short":"L. Dello Schiavo, K. Suzuki, Journal of Functional Analysis 281 (2021).","apa":"Dello Schiavo, L., &#38; Suzuki, K. (2021). Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local Dirichlet spaces. <i>Journal of Functional Analysis</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jfa.2021.109234\">https://doi.org/10.1016/j.jfa.2021.109234</a>","ieee":"L. Dello Schiavo and K. Suzuki, “Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local Dirichlet spaces,” <i>Journal of Functional Analysis</i>, vol. 281, no. 11. Elsevier, 2021.","chicago":"Dello Schiavo, Lorenzo, and Kohei Suzuki. “Rademacher-Type Theorems and Sobolev-to-Lipschitz Properties for Strongly Local Dirichlet Spaces.” <i>Journal of Functional Analysis</i>. Elsevier, 2021. <a href=\"https://doi.org/10.1016/j.jfa.2021.109234\">https://doi.org/10.1016/j.jfa.2021.109234</a>.","ama":"Dello Schiavo L, Suzuki K. Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local Dirichlet spaces. <i>Journal of Functional Analysis</i>. 2021;281(11). doi:<a href=\"https://doi.org/10.1016/j.jfa.2021.109234\">10.1016/j.jfa.2021.109234</a>","mla":"Dello Schiavo, Lorenzo, and Kohei Suzuki. “Rademacher-Type Theorems and Sobolev-to-Lipschitz Properties for Strongly Local Dirichlet Spaces.” <i>Journal of Functional Analysis</i>, vol. 281, no. 11, 109234, Elsevier, 2021, doi:<a href=\"https://doi.org/10.1016/j.jfa.2021.109234\">10.1016/j.jfa.2021.109234</a>.","ista":"Dello Schiavo L, Suzuki K. 2021. Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local Dirichlet spaces. Journal of Functional Analysis. 281(11), 109234."},"type":"journal_article","article_type":"original","status":"public","language":[{"iso":"eng"}],"publication_status":"published","abstract":[{"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.","lang":"eng"}],"quality_controlled":"1","publication":"Journal of Functional Analysis","external_id":{"isi":["000703896600005"],"arxiv":["2008.01492"]},"date_created":"2021-10-03T22:01:21Z","project":[{"name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"},{"grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics"}],"_id":"10070","month":"09","date_updated":"2023-08-14T07:05:44Z","title":"Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local Dirichlet spaces","ec_funded":1,"article_processing_charge":"No","date_published":"2021-09-15T00:00:00Z","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2008.01492"}],"volume":281,"intvolume":"       281","oa":1,"issue":"11","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.","article_number":"109234"},{"author":[{"first_name":"Joe P.","full_name":"Chen, Joe P.","last_name":"Chen"},{"id":"E1836206-9F16-11E9-8814-AEFDE5697425","first_name":"Federico","full_name":"Sau, Federico","last_name":"Sau"}],"year":"2021","publication_identifier":{"issn":["1024-2953"]},"department":[{"_id":"JaMa"}],"publisher":"Polymat Publishing","day":"16","arxiv":1,"oa_version":"Preprint","quality_controlled":"1","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."}],"publication_status":"published","language":[{"iso":"eng"}],"status":"public","article_type":"original","type":"journal_article","citation":{"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.","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.","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.","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.","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.","short":"J.P. Chen, F. Sau, Markov Processes And Related Fields 27 (2021) 339–380.","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."},"date_published":"2021-03-16T00:00:00Z","keyword":["interacting particle systems","higher-order fields","hydrodynamic limit","equilibrium fluctuations","duality"],"article_processing_charge":"No","ec_funded":1,"date_updated":"2022-01-10T15:29:08Z","title":"Higher-order hydrodynamics and equilibrium fluctuations of interacting particle systems","month":"03","_id":"10613","project":[{"call_identifier":"H2020","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships"}],"date_created":"2022-01-10T14:02:31Z","external_id":{"arxiv":["2008.13403"]},"publication":"Markov Processes And Related Fields","page":"339-380","issue":"3","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","oa":1,"intvolume":"        27","volume":27,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2008.13403"}],"related_material":{"link":[{"description":"Link to Abstract on publisher's website","url":"http://math-mprf.org/journal/articles/id1614/","relation":"other"},{"relation":"used_for_analysis_in","url":"https://arxiv.org/abs/2004.08412","description":"Referred to in Abstract"}]}},{"oa":1,"intvolume":"        64","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","issue":"3","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.","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1017/S0013091521000080"}],"volume":64,"scopus_import":"1","article_processing_charge":"No","date_published":"2021-08-01T00:00:00Z","date_updated":"2023-08-17T07:12:05Z","title":"Self-adjoint extensions of bipartite Hamiltonians","month":"08","_id":"9627","external_id":{"arxiv":["1912.03670"],"isi":["000721363700003"]},"date_created":"2021-07-04T22:01:24Z","publication":"Proceedings of the Edinburgh Mathematical Society","page":"443-447","quality_controlled":"1","publication_status":"published","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"}],"status":"public","language":[{"iso":"eng"}],"article_type":"original","type":"journal_article","citation":{"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>.","ista":"Lenz D, Weinmann T, Wirth M. 2021. Self-adjoint extensions of bipartite Hamiltonians. Proceedings of the Edinburgh Mathematical Society. 64(3), 443–447.","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>.","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.","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>","short":"D. Lenz, T. Weinmann, M. Wirth, Proceedings of the Edinburgh Mathematical Society 64 (2021) 443–447."},"year":"2021","author":[{"last_name":"Lenz","full_name":"Lenz, Daniel","first_name":"Daniel"},{"first_name":"Timon","full_name":"Weinmann, Timon","last_name":"Weinmann"},{"first_name":"Melchior","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","last_name":"Wirth","orcid":"0000-0002-0519-4241","full_name":"Wirth, Melchior"}],"isi":1,"department":[{"_id":"JaMa"}],"publication_identifier":{"issn":["0013-0915"],"eissn":["1464-3839"]},"publisher":"Cambridge University Press","day":"01","doi":"10.1017/S0013091521000080","oa_version":"Published Version","arxiv":1},{"day":"20","publisher":"Institute of Science and Technology Austria","oa_version":"Published Version","doi":"10.15479/at:ista:9733","author":[{"first_name":"Dario","id":"41A639AA-F248-11E8-B48F-1D18A9856A87","full_name":"Feliciangeli, Dario","orcid":"0000-0003-0754-8530","last_name":"Feliciangeli"}],"year":"2021","tmp":{"image":"/image/cc_by_nd.png","name":"Creative Commons Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nd/4.0/legalcode","short":"CC BY-ND (4.0)"},"degree_awarded":"PhD","department":[{"_id":"GradSch"},{"_id":"RoSe"},{"_id":"JaMa"}],"publication_identifier":{"issn":["2663-337X"]},"ddc":["515","519","539"],"type":"dissertation","citation":{"short":"D. Feliciangeli, The Polaron at Strong Coupling, Institute of Science and Technology Austria, 2021.","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.","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>","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>.","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>.","ista":"Feliciangeli D. 2021. The polaron at strong coupling. Institute of Science and Technology Austria."},"file":[{"file_id":"9944","date_created":"2021-08-19T14:03:48Z","creator":"dfelicia","file_size":1958710,"content_type":"application/pdf","date_updated":"2021-09-06T09:28:56Z","relation":"main_file","checksum":"e88bb8ca43948abe060eb2d2fa719881","access_level":"open_access","file_name":"Thesis_FeliciangeliA.pdf"},{"file_size":3771669,"content_type":"application/octet-stream","date_updated":"2022-03-10T12:13:57Z","relation":"source_file","checksum":"72810843abee83705853505b3f8348aa","access_level":"closed","file_name":"thesis.7z","file_id":"9945","date_created":"2021-08-19T14:06:35Z","creator":"dfelicia"}],"language":[{"iso":"eng"}],"has_accepted_license":"1","status":"public","abstract":[{"lang":"eng","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."}],"publication_status":"published","date_created":"2021-07-27T15:48:30Z","project":[{"name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117","call_identifier":"H2020"},{"call_identifier":"H2020","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","grant_number":"694227","name":"Analysis of quantum many-body systems"},{"name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"}],"_id":"9733","page":"180","file_date_updated":"2022-03-10T12:13:57Z","supervisor":[{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","orcid":"0000-0002-6781-0521","full_name":"Seiringer, Robert","last_name":"Seiringer"},{"full_name":"Maas, Jan","orcid":"0000-0002-0845-1338","last_name":"Maas","first_name":"Jan","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87"}],"ec_funded":1,"date_published":"2021-08-20T00:00:00Z","article_processing_charge":"No","month":"08","title":"The polaron at strong coupling","date_updated":"2024-03-06T12:30:44Z","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","oa":1,"alternative_title":["ISTA Thesis"],"related_material":{"record":[{"relation":"part_of_dissertation","status":"public","id":"9787"},{"id":"9792","relation":"part_of_dissertation","status":"public"},{"relation":"part_of_dissertation","status":"public","id":"9225"},{"relation":"part_of_dissertation","status":"public","id":"9781"},{"id":"9791","status":"public","relation":"part_of_dissertation"}]}},{"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2106.11217"}],"related_material":{"record":[{"id":"9733","relation":"dissertation_contains","status":"public"},{"status":"public","relation":"dissertation_contains","id":"10030"},{"status":"public","relation":"later_version","id":"12911"}]},"article_number":"2106.11217","oa":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].","title":"A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature","date_updated":"2023-11-14T13:21:01Z","month":"07","article_processing_charge":"No","date_published":"2021-07-21T00:00:00Z","ec_funded":1,"publication":"arXiv","project":[{"name":"Analysis of quantum many-body systems","call_identifier":"H2020","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","grant_number":"694227"},{"grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics"},{"name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"}],"_id":"9792","external_id":{"arxiv":["2106.11217"]},"date_created":"2021-08-06T09:07:12Z","publication_status":"submitted","abstract":[{"lang":"eng","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."}],"status":"public","has_accepted_license":"1","language":[{"iso":"eng"}],"citation":{"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>","short":"D. Feliciangeli, A. Gerolin, L. Portinale, ArXiv (n.d.).","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>. .","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>.","ista":"Feliciangeli D, Gerolin A, Portinale L. A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature. arXiv, 2106.11217.","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>."},"type":"preprint","ddc":["510"],"department":[{"_id":"RoSe"},{"_id":"JaMa"}],"tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"year":"2021","author":[{"first_name":"Dario","id":"41A639AA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-0754-8530","full_name":"Feliciangeli, Dario","last_name":"Feliciangeli"},{"full_name":"Gerolin, Augusto","last_name":"Gerolin","first_name":"Augusto"},{"first_name":"Lorenzo","id":"30AD2CBC-F248-11E8-B48F-1D18A9856A87","last_name":"Portinale","full_name":"Portinale, Lorenzo"}],"doi":"10.48550/arXiv.2106.11217","oa_version":"Preprint","arxiv":1,"day":"21"},{"acknowledgement":"Both authors would like to thank Jan Maas for fruitful discussions and helpful comments.","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa":1,"intvolume":"       387","volume":387,"scopus_import":"1","date_published":"2021-08-30T00:00:00Z","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"article_processing_charge":"Yes (via OA deal)","ec_funded":1,"title":"Complete gradient estimates of quantum Markov semigroups","date_updated":"2023-08-11T11:09:07Z","month":"08","project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"},{"call_identifier":"H2020","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships"},{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems"}],"_id":"9973","date_created":"2021-08-30T10:07:44Z","external_id":{"isi":["000691214200001"],"arxiv":["2007.13506"]},"file_date_updated":"2021-09-08T09:46:34Z","publication":"Communications in Mathematical Physics","page":"761–791","quality_controlled":"1","publication_status":"published","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"}],"language":[{"iso":"eng"}],"status":"public","has_accepted_license":"1","ddc":["621"],"article_type":"original","file":[{"file_size":505971,"date_updated":"2021-09-08T09:46:34Z","content_type":"application/pdf","relation":"main_file","checksum":"8a602f916b1c2b0dc1159708b7cb204b","access_level":"open_access","file_name":"2021_CommunMathPhys_Wirth.pdf","file_id":"9990","creator":"cchlebak","date_created":"2021-09-08T07:34:24Z"}],"type":"journal_article","citation":{"ista":"Wirth M, Zhang H. 2021. Complete gradient estimates of quantum Markov semigroups. Communications in Mathematical Physics. 387, 761–791.","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>.","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>","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.","short":"M. Wirth, H. Zhang, Communications in Mathematical Physics 387 (2021) 761–791.","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>"},"isi":1,"author":[{"first_name":"Melchior","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","orcid":"0000-0002-0519-4241","full_name":"Wirth, Melchior","last_name":"Wirth"},{"first_name":"Haonan","id":"D8F41E38-9E66-11E9-A9E2-65C2E5697425","full_name":"Zhang, Haonan","last_name":"Zhang"}],"year":"2021","department":[{"_id":"JaMa"}],"publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"publisher":"Springer Nature","day":"30","doi":"10.1007/s00220-021-04199-4","arxiv":1,"oa_version":"Published Version"},{"month":"10","date_updated":"2023-08-22T10:32:29Z","title":"Equality conditions of data processing inequality for α-z Rényi relative entropies","ec_funded":1,"article_processing_charge":"No","date_published":"2020-10-01T00:00:00Z","publication":"Journal of Mathematical Physics","external_id":{"isi":["000578529200001"],"arxiv":["2007.06644"]},"date_created":"2020-10-18T22:01:36Z","_id":"8670","project":[{"name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"main_file_link":[{"url":"https://arxiv.org/abs/2007.06644","open_access":"1"}],"volume":61,"oa":1,"intvolume":"        61","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.","issue":"10","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_number":"102201","scopus_import":"1","publication_identifier":{"issn":["00222488"]},"department":[{"_id":"JaMa"}],"year":"2020","author":[{"last_name":"Zhang","full_name":"Zhang, Haonan","id":"D8F41E38-9E66-11E9-A9E2-65C2E5697425","first_name":"Haonan"}],"isi":1,"arxiv":1,"oa_version":"Preprint","doi":"10.1063/5.0022787","day":"01","publisher":"AIP Publishing","status":"public","language":[{"iso":"eng"}],"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)]."}],"publication_status":"published","quality_controlled":"1","type":"journal_article","citation":{"short":"H. Zhang, Journal of Mathematical Physics 61 (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>","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.","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>","ista":"Zhang H. 2020. Equality conditions of data processing inequality for α-z Rényi relative entropies. Journal of Mathematical Physics. 61(10), 102201.","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>."},"article_type":"original"},{"title":"Modeling of chemical reaction systems with detailed balance using gradient structures","date_updated":"2023-08-22T13:24:27Z","month":"12","date_published":"2020-12-01T00:00:00Z","article_processing_charge":"No","ec_funded":1,"file_date_updated":"2021-02-04T10:29:11Z","publication":"Journal of Statistical Physics","page":"2257-2303","_id":"8758","project":[{"name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"_id":"260482E2-B435-11E9-9278-68D0E5697425","grant_number":" F06504","call_identifier":"FWF","name":"Taming Complexity in Partial Di erential Systems"}],"date_created":"2020-11-15T23:01:18Z","external_id":{"arxiv":["2004.02831"],"isi":["000587107200002"]},"volume":181,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","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).","issue":"6","intvolume":"       181","oa":1,"scopus_import":"1","department":[{"_id":"JaMa"}],"publication_identifier":{"eissn":["15729613"],"issn":["00224715"]},"tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"author":[{"first_name":"Jan","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-0845-1338","full_name":"Maas, Jan","last_name":"Maas"},{"full_name":"Mielke, Alexander","last_name":"Mielke","first_name":"Alexander"}],"isi":1,"year":"2020","doi":"10.1007/s10955-020-02663-4","oa_version":"Published Version","arxiv":1,"publisher":"Springer Nature","day":"01","abstract":[{"lang":"eng","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."}],"publication_status":"published","language":[{"iso":"eng"}],"has_accepted_license":"1","status":"public","quality_controlled":"1","file":[{"creator":"dernst","date_created":"2021-02-04T10:29:11Z","file_id":"9087","file_name":"2020_JourStatPhysics_Maas.pdf","success":1,"access_level":"open_access","relation":"main_file","checksum":"bc2b63a90197b97cbc73eccada4639f5","date_updated":"2021-02-04T10:29:11Z","content_type":"application/pdf","file_size":753596}],"type":"journal_article","citation":{"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.","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>.","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.","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>","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>."},"ddc":["510"],"article_type":"original"},{"article_number":"138","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).","oa":1,"intvolume":"        25","volume":25,"scopus_import":"1","date_published":"2020-10-21T00:00:00Z","article_processing_charge":"No","ec_funded":1,"date_updated":"2023-10-17T12:51:56Z","title":"Symmetric simple exclusion process in dynamic environment: Hydrodynamics","month":"10","project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships"}],"_id":"8973","date_created":"2020-12-27T23:01:17Z","external_id":{"isi":["000591737500001"],"arxiv":["1811.01366"]},"file_date_updated":"2020-12-28T08:24:08Z","publication":"Electronic Journal of Probability","quality_controlled":"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."}],"publication_status":"published","language":[{"iso":"eng"}],"has_accepted_license":"1","status":"public","ddc":["510"],"article_type":"original","file":[{"file_id":"8976","date_created":"2020-12-28T08:24:08Z","creator":"dernst","date_updated":"2020-12-28T08:24:08Z","content_type":"application/pdf","file_size":696653,"relation":"main_file","checksum":"d75359b9814e78d57c0a481b7cde3751","success":1,"access_level":"open_access","file_name":"2020_ElectronJProbab_Redig.pdf"}],"citation":{"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>.","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>","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)."},"type":"journal_article","isi":1,"author":[{"full_name":"Redig, Frank","last_name":"Redig","first_name":"Frank"},{"last_name":"Saada","full_name":"Saada, Ellen","first_name":"Ellen"},{"full_name":"Sau, Federico","last_name":"Sau","id":"E1836206-9F16-11E9-8814-AEFDE5697425","first_name":"Federico"}],"year":"2020","department":[{"_id":"JaMa"}],"publication_identifier":{"eissn":["1083-6489"]},"publisher":" Institute of Mathematical Statistics","day":"21","doi":"10.1214/20-EJP536","arxiv":1,"oa_version":"Published Version"},{"arxiv":1,"oa_version":"Preprint","doi":"10.1137/19M1243440","day":"01","publisher":"Society for Industrial and Applied Mathematics","publication_identifier":{"eissn":["10957154"],"issn":["00361410"]},"department":[{"_id":"JaMa"}],"year":"2020","author":[{"first_name":"Peter","full_name":"Gladbach, Peter","last_name":"Gladbach"},{"last_name":"Kopfer","full_name":"Kopfer, Eva","first_name":"Eva"},{"first_name":"Jan","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","last_name":"Maas","full_name":"Maas, Jan","orcid":"0000-0002-0845-1338"}],"isi":1,"type":"journal_article","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.","short":"P. Gladbach, E. Kopfer, J. Maas, SIAM Journal on Mathematical Analysis 52 (2020) 2759–2802.","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>","ista":"Gladbach P, Kopfer E, Maas J. 2020. Scaling limits of discrete optimal transport. SIAM Journal on Mathematical Analysis. 52(3), 2759–2802.","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>","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>."},"article_type":"original","status":"public","language":[{"iso":"eng"}],"publist_id":"7983","publication_status":"published","abstract":[{"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.","lang":"eng"}],"quality_controlled":"1","page":"2759-2802","publication":"SIAM Journal on Mathematical Analysis","external_id":{"arxiv":["1809.01092"],"isi":["000546975100017"]},"date_created":"2018-12-11T11:44:28Z","_id":"71","month":"10","title":"Scaling limits of discrete optimal transport","date_updated":"2023-09-18T08:13:15Z","article_processing_charge":"No","date_published":"2020-10-01T00:00:00Z","scopus_import":"1","main_file_link":[{"url":"https://arxiv.org/abs/1809.01092","open_access":"1"}],"volume":52,"intvolume":"        52","oa":1,"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","issue":"3"},{"main_file_link":[{"url":"https://arxiv.org/abs/1902.07635","open_access":"1"}],"volume":37,"oa":1,"intvolume":"        37","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","issue":"3","scopus_import":"1","date_updated":"2023-08-17T14:35:46Z","title":"Nondivergence form quasilinear heat equations driven by space-time white noise","month":"05","article_processing_charge":"No","date_published":"2020-05-01T00:00:00Z","publication":"Annales de l'Institut Henri Poincaré C, Analyse non linéaire","page":"663-682","_id":"7388","external_id":{"arxiv":["1902.07635"],"isi":["000531049800007"]},"date_created":"2020-01-29T09:39:41Z","publication_status":"published","abstract":[{"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.","lang":"eng"}],"status":"public","language":[{"iso":"eng"}],"quality_controlled":"1","type":"journal_article","citation":{"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>","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>.","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>.","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.","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>","short":"M. Gerencser, Annales de l’Institut Henri Poincaré C, Analyse Non Linéaire 37 (2020) 663–682.","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."},"article_type":"original","publication_identifier":{"issn":["0294-1449"]},"department":[{"_id":"JaMa"}],"year":"2020","isi":1,"author":[{"first_name":"Mate","id":"44ECEDF2-F248-11E8-B48F-1D18A9856A87","full_name":"Gerencser, Mate","last_name":"Gerencser"}],"doi":"10.1016/j.anihpc.2020.01.003","oa_version":"Preprint","arxiv":1,"publisher":"Elsevier","day":"01"},{"intvolume":"      2256","oa":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","main_file_link":[{"url":"https://arxiv.org/abs/1808.07350","open_access":"1"}],"volume":2256,"scopus_import":"1","article_processing_charge":"No","date_published":"2020-06-21T00:00:00Z","ec_funded":1,"date_updated":"2023-08-17T13:48:31Z","title":"Gromov's waist of non-radial Gaussian measures and radial non-Gaussian measures","month":"06","_id":"74","project":[{"name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117"}],"external_id":{"arxiv":["1808.07350"],"isi":["000557689300003"]},"date_created":"2018-12-11T11:44:29Z","publication":"Geometric Aspects of Functional Analysis","page":"1-27","quality_controlled":"1","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"}],"publication_status":"published","status":"public","language":[{"iso":"eng"}],"type":"book_chapter","citation":{"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>","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>.","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.","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>.","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>","short":"A. Akopyan, R. Karasev, in:, B. Klartag, E. Milman (Eds.), Geometric Aspects of Functional Analysis, Springer Nature, 2020, pp. 1–27.","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."},"year":"2020","isi":1,"author":[{"first_name":"Arseniy","id":"430D2C90-F248-11E8-B48F-1D18A9856A87","last_name":"Akopyan","orcid":"0000-0002-2548-617X","full_name":"Akopyan, Arseniy"},{"last_name":"Karasev","full_name":"Karasev, Roman","first_name":"Roman"}],"editor":[{"full_name":"Klartag, Bo'az","last_name":"Klartag","first_name":"Bo'az"},{"full_name":"Milman, Emanuel","last_name":"Milman","first_name":"Emanuel"}],"publication_identifier":{"eissn":["16179692"],"eisbn":["9783030360207"],"issn":["00758434"],"isbn":["9783030360191"]},"department":[{"_id":"HeEd"},{"_id":"JaMa"}],"series_title":"LNM","publisher":"Springer Nature","day":"21","doi":"10.1007/978-3-030-36020-7_1","oa_version":"Preprint","arxiv":1},{"oa_version":"Preprint","arxiv":1,"doi":"10.1016/j.aim.2020.107053","day":"13","publisher":"Elsevier","department":[{"_id":"JaMa"}],"year":"2020","author":[{"first_name":"Haonan","id":"D8F41E38-9E66-11E9-A9E2-65C2E5697425","full_name":"Zhang, Haonan","last_name":"Zhang"}],"isi":1,"type":"journal_article","citation":{"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>","short":"H. Zhang, Advances in Mathematics 365 (2020).","ieee":"H. Zhang, “From Wigner-Yanase-Dyson conjecture to Carlen-Frank-Lieb conjecture,” <i>Advances in Mathematics</i>, vol. 365. Elsevier, 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>","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>.","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>.","ista":"Zhang H. 2020. From Wigner-Yanase-Dyson conjecture to Carlen-Frank-Lieb conjecture. Advances in Mathematics. 365, 107053."},"article_type":"original","ddc":["515"],"status":"public","language":[{"iso":"eng"}],"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. "}],"publication_status":"published","quality_controlled":"1","publication":"Advances in Mathematics","external_id":{"arxiv":["1811.01205"],"isi":["000522798000001"]},"date_created":"2020-02-23T21:43:50Z","_id":"7509","project":[{"call_identifier":"H2020","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships"}],"month":"05","date_updated":"2023-08-18T06:37:09Z","title":"From Wigner-Yanase-Dyson conjecture to Carlen-Frank-Lieb conjecture","ec_funded":1,"article_processing_charge":"No","date_published":"2020-05-13T00:00:00Z","main_file_link":[{"url":"https://arxiv.org/abs/1811.01205","open_access":"1"}],"volume":365,"oa":1,"intvolume":"       365","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.","article_number":"107053"}]