[{"date_updated":"2022-01-10T15:29:08Z","department":[{"_id":"JaMa"}],"_id":"10613","keyword":["interacting particle systems","higher-order fields","hydrodynamic limit","equilibrium fluctuations","duality"],"status":"public","article_type":"original","type":"journal_article","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["1024-2953"]},"ec_funded":1,"issue":"3","related_material":{"link":[{"url":"http://math-mprf.org/journal/articles/id1614/","relation":"other","description":"Link to Abstract on publisher's website"},{"url":"https://arxiv.org/abs/2004.08412","relation":"used_for_analysis_in","description":"Referred to in Abstract"}]},"volume":27,"oa_version":"Preprint","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."}],"intvolume":" 27","month":"03","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2008.13403"}],"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","citation":{"mla":"Chen, Joe P., and Federico Sau. “Higher-Order Hydrodynamics and Equilibrium Fluctuations of Interacting Particle Systems.” Markov Processes And Related Fields, vol. 27, no. 3, Polymat Publishing, 2021, pp. 339–80.","ama":"Chen JP, Sau F. Higher-order hydrodynamics and equilibrium fluctuations of interacting particle systems. Markov Processes And Related Fields. 2021;27(3):339-380.","apa":"Chen, J. P., & Sau, F. (2021). Higher-order hydrodynamics and equilibrium fluctuations of interacting particle systems. Markov Processes And Related Fields. 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,” Markov Processes And Related Fields, vol. 27, no. 3. Polymat Publishing, pp. 339–380, 2021.","chicago":"Chen, Joe P., and Federico Sau. “Higher-Order Hydrodynamics and Equilibrium Fluctuations of Interacting Particle Systems.” Markov Processes And Related Fields. Polymat Publishing, 2021.","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."},"title":"Higher-order hydrodynamics and equilibrium fluctuations of interacting particle systems","external_id":{"arxiv":["2008.13403"]},"article_processing_charge":"No","author":[{"full_name":"Chen, Joe P.","last_name":"Chen","first_name":"Joe P."},{"first_name":"Federico","id":"E1836206-9F16-11E9-8814-AEFDE5697425","full_name":"Sau, Federico","last_name":"Sau"}],"project":[{"call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"}],"publication":"Markov Processes And Related Fields","day":"16","year":"2021","date_created":"2022-01-10T14:02:31Z","date_published":"2021-03-16T00:00:00Z","page":"339-380","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,"publisher":"Polymat Publishing","quality_controlled":"1"},{"department":[{"_id":"JaMa"}],"file_date_updated":"2021-09-08T09:46:34Z","date_updated":"2023-08-11T11:09:07Z","ddc":["621"],"article_type":"original","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"_id":"9973","volume":387,"ec_funded":1,"publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"publication_status":"published","file":[{"creator":"cchlebak","date_updated":"2021-09-08T09:46:34Z","file_size":505971,"date_created":"2021-09-08T07:34:24Z","file_name":"2021_CommunMathPhys_Wirth.pdf","access_level":"open_access","relation":"main_file","content_type":"application/pdf","checksum":"8a602f916b1c2b0dc1159708b7cb204b","file_id":"9990"}],"language":[{"iso":"eng"}],"scopus_import":"1","month":"08","intvolume":" 387","abstract":[{"lang":"eng","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."}],"oa_version":"Published Version","author":[{"full_name":"Wirth, Melchior","orcid":"0000-0002-0519-4241","last_name":"Wirth","first_name":"Melchior","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E"},{"id":"D8F41E38-9E66-11E9-A9E2-65C2E5697425","first_name":"Haonan","last_name":"Zhang","full_name":"Zhang, Haonan"}],"article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000691214200001"],"arxiv":["2007.13506"]},"title":"Complete gradient estimates of quantum Markov semigroups","citation":{"chicago":"Wirth, Melchior, and Haonan Zhang. “Complete Gradient Estimates of Quantum Markov Semigroups.” Communications in Mathematical Physics. 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Elsevier, 2021. https://doi.org/10.1016/j.spa.2021.08.006.","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.","mla":"Floreani, Simone, et al. “Hydrodynamics for the Partial Exclusion Process in Random Environment.” Stochastic Processes and Their Applications, vol. 142, Elsevier, 2021, pp. 124–58, doi:10.1016/j.spa.2021.08.006.","ieee":"S. Floreani, F. Redig, and F. Sau, “Hydrodynamics for the partial exclusion process in random environment,” Stochastic Processes and their Applications, 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., & Sau, F. (2021). Hydrodynamics for the partial exclusion process in random environment. Stochastic Processes and Their Applications. Elsevier. https://doi.org/10.1016/j.spa.2021.08.006","ama":"Floreani S, Redig F, Sau F. Hydrodynamics for the partial exclusion process in random environment. Stochastic Processes and their Applications. 2021;142:124-158. doi:10.1016/j.spa.2021.08.006"},"project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships"}],"date_created":"2021-09-19T22:01:25Z","doi":"10.1016/j.spa.2021.08.006","date_published":"2021-08-27T00:00:00Z","page":"124-158","publication":"Stochastic Processes and their Applications","day":"27","year":"2021","isi":1,"has_accepted_license":"1","oa":1,"publisher":"Elsevier","quality_controlled":"1","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.","department":[{"_id":"JaMa"}],"file_date_updated":"2022-05-13T07:55:50Z","ddc":["519"],"date_updated":"2023-08-14T06:52:43Z","keyword":["hydrodynamic limit","random environment","random conductance model","arbitrary starting point quenched invariance principle","duality","mild solution"],"status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","article_type":"original","_id":"10024","ec_funded":1,"volume":142,"language":[{"iso":"eng"}],"file":[{"success":1,"checksum":"56768c553d7218ee5714902ffec90ec4","file_id":"11370","relation":"main_file","access_level":"open_access","content_type":"application/pdf","file_name":"2021_StochasticProcessesAppl_Floreani.pdf","date_created":"2022-05-13T07:55:50Z","creator":"dernst","file_size":2115791,"date_updated":"2022-05-13T07:55:50Z"}],"publication_status":"published","publication_identifier":{"issn":["0304-4149"]},"intvolume":" 142","month":"08","scopus_import":"1","oa_version":"Published Version","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"}]},{"oa":1,"quality_controlled":"1","publisher":"Elsevier","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.","date_created":"2021-10-03T22:01:21Z","date_published":"2021-09-15T00:00:00Z","doi":"10.1016/j.jfa.2021.109234","publication":"Journal of Functional Analysis","day":"15","year":"2021","isi":1,"project":[{"name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"},{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117"}],"article_number":"109234","title":"Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local Dirichlet spaces","external_id":{"isi":["000703896600005"],"arxiv":["2008.01492"]},"article_processing_charge":"No","author":[{"first_name":"Lorenzo","id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","last_name":"Dello Schiavo","orcid":"0000-0002-9881-6870","full_name":"Dello Schiavo, Lorenzo"},{"first_name":"Kohei","last_name":"Suzuki","full_name":"Suzuki, Kohei"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"chicago":"Dello Schiavo, Lorenzo, and Kohei Suzuki. “Rademacher-Type Theorems and Sobolev-to-Lipschitz Properties for Strongly Local Dirichlet Spaces.” Journal of Functional Analysis. Elsevier, 2021. https://doi.org/10.1016/j.jfa.2021.109234.","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.","mla":"Dello Schiavo, Lorenzo, and Kohei Suzuki. “Rademacher-Type Theorems and Sobolev-to-Lipschitz Properties for Strongly Local Dirichlet Spaces.” Journal of Functional Analysis, vol. 281, no. 11, 109234, Elsevier, 2021, doi:10.1016/j.jfa.2021.109234.","apa":"Dello Schiavo, L., & Suzuki, K. (2021). Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local Dirichlet spaces. Journal of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2021.109234","ama":"Dello Schiavo L, Suzuki K. Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local Dirichlet spaces. Journal of Functional Analysis. 2021;281(11). doi:10.1016/j.jfa.2021.109234","ieee":"L. Dello Schiavo and K. Suzuki, “Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local Dirichlet spaces,” Journal of Functional Analysis, vol. 281, no. 11. Elsevier, 2021.","short":"L. Dello Schiavo, K. Suzuki, Journal of Functional Analysis 281 (2021)."},"intvolume":" 281","month":"09","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2008.01492","open_access":"1"}],"scopus_import":"1","oa_version":"Preprint","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"}],"ec_funded":1,"issue":"11","volume":281,"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["0022-1236"],"eissn":["1096-0783"]},"status":"public","type":"journal_article","article_type":"original","_id":"10070","department":[{"_id":"JaMa"}],"date_updated":"2023-08-14T07:05:44Z"},{"citation":{"ista":"Lenz D, Weinmann T, Wirth M. 2021. Self-adjoint extensions of bipartite Hamiltonians. Proceedings of the Edinburgh Mathematical Society. 64(3), 443–447.","chicago":"Lenz, Daniel, Timon Weinmann, and Melchior Wirth. “Self-Adjoint Extensions of Bipartite Hamiltonians.” Proceedings of the Edinburgh Mathematical Society. Cambridge University Press, 2021. https://doi.org/10.1017/S0013091521000080.","apa":"Lenz, D., Weinmann, T., & Wirth, M. (2021). Self-adjoint extensions of bipartite Hamiltonians. Proceedings of the Edinburgh Mathematical Society. Cambridge University Press. https://doi.org/10.1017/S0013091521000080","ama":"Lenz D, Weinmann T, Wirth M. Self-adjoint extensions of bipartite Hamiltonians. Proceedings of the Edinburgh Mathematical Society. 2021;64(3):443-447. doi:10.1017/S0013091521000080","ieee":"D. Lenz, T. Weinmann, and M. Wirth, “Self-adjoint extensions of bipartite Hamiltonians,” Proceedings of the Edinburgh Mathematical Society, vol. 64, no. 3. Cambridge University Press, pp. 443–447, 2021.","short":"D. Lenz, T. Weinmann, M. Wirth, Proceedings of the Edinburgh Mathematical Society 64 (2021) 443–447.","mla":"Lenz, Daniel, et al. “Self-Adjoint Extensions of Bipartite Hamiltonians.” Proceedings of the Edinburgh Mathematical Society, vol. 64, no. 3, Cambridge University Press, 2021, pp. 443–47, doi:10.1017/S0013091521000080."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","external_id":{"arxiv":["1912.03670"],"isi":["000721363700003"]},"article_processing_charge":"No","author":[{"first_name":"Daniel","full_name":"Lenz, Daniel","last_name":"Lenz"},{"first_name":"Timon","last_name":"Weinmann","full_name":"Weinmann, Timon"},{"full_name":"Wirth, Melchior","orcid":"0000-0002-0519-4241","last_name":"Wirth","first_name":"Melchior","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E"}],"title":"Self-adjoint extensions of bipartite Hamiltonians","year":"2021","isi":1,"publication":"Proceedings of the Edinburgh Mathematical Society","day":"01","page":"443-447","date_created":"2021-07-04T22:01:24Z","date_published":"2021-08-01T00:00:00Z","doi":"10.1017/S0013091521000080","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.","oa":1,"publisher":"Cambridge University Press","quality_controlled":"1","date_updated":"2023-08-17T07:12:05Z","department":[{"_id":"JaMa"}],"_id":"9627","article_type":"original","type":"journal_article","status":"public","publication_status":"published","publication_identifier":{"issn":["0013-0915"],"eissn":["1464-3839"]},"language":[{"iso":"eng"}],"issue":"3","volume":64,"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"}],"oa_version":"Published Version","main_file_link":[{"url":"https://doi.org/10.1017/S0013091521000080","open_access":"1"}],"scopus_import":"1","intvolume":" 64","month":"08"}]