[{"author":[{"first_name":"Asbjørn Bækgaard","orcid":"0000-0003-4476-2288","last_name":"Lauritsen","full_name":"Lauritsen, Asbjørn Bækgaard","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1"},{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","orcid":"0000-0002-6781-0521","last_name":"Seiringer","full_name":"Seiringer, Robert"}],"abstract":[{"lang":"eng","text":"We prove an upper bound on the ground state energy of the dilute spin-polarized Fermi gas capturing the leading correction to the kinetic energy resulting from repulsive interactions. One of the main ingredients in the proof is a rigorous implementation of the fermionic cluster expansion of Gaudin et al. (1971) [15]."}],"citation":{"short":"A.B. Lauritsen, R. Seiringer, Journal of Functional Analysis 286 (2024).","ista":"Lauritsen AB, Seiringer R. 2024. Ground state energy of the dilute spin-polarized Fermi gas: Upper bound via cluster expansion. Journal of Functional Analysis. 286(7), 110320.","ama":"Lauritsen AB, Seiringer R. Ground state energy of the dilute spin-polarized Fermi gas: Upper bound via cluster expansion. <i>Journal of Functional Analysis</i>. 2024;286(7). doi:<a href=\"https://doi.org/10.1016/j.jfa.2024.110320\">10.1016/j.jfa.2024.110320</a>","mla":"Lauritsen, Asbjørn Bækgaard, and Robert Seiringer. “Ground State Energy of the Dilute Spin-Polarized Fermi Gas: Upper Bound via Cluster Expansion.” <i>Journal of Functional Analysis</i>, vol. 286, no. 7, 110320, Elsevier, 2024, doi:<a href=\"https://doi.org/10.1016/j.jfa.2024.110320\">10.1016/j.jfa.2024.110320</a>.","chicago":"Lauritsen, Asbjørn Bækgaard, and Robert Seiringer. “Ground State Energy of the Dilute Spin-Polarized Fermi Gas: Upper Bound via Cluster Expansion.” <i>Journal of Functional Analysis</i>. Elsevier, 2024. <a href=\"https://doi.org/10.1016/j.jfa.2024.110320\">https://doi.org/10.1016/j.jfa.2024.110320</a>.","apa":"Lauritsen, A. B., &#38; Seiringer, R. (2024). Ground state energy of the dilute spin-polarized Fermi gas: Upper bound via cluster expansion. <i>Journal of Functional Analysis</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jfa.2024.110320\">https://doi.org/10.1016/j.jfa.2024.110320</a>","ieee":"A. B. Lauritsen and R. Seiringer, “Ground state energy of the dilute spin-polarized Fermi gas: Upper bound via cluster expansion,” <i>Journal of Functional Analysis</i>, vol. 286, no. 7. Elsevier, 2024."},"publication_status":"epub_ahead","quality_controlled":"1","project":[{"grant_number":"694227","name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"_id":"bda63fe5-d553-11ed-ba76-a16e3d2f256b","name":"Mathematical Challenges in BCS Theory of Superconductivity","grant_number":"I06427"}],"oa_version":"Published Version","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","acknowledgement":"A.B.L. would like to thank Johannes Agerskov and Jan Philip Solovej for valuable discussions. We thank Alessandro Giuliani for helpful discussions and for pointing out the reference [18]. Funding from the European Union's Horizon 2020 research and innovation programme under the ERC grant agreement No 694227 is acknowledged. Financial support by the Austrian Science Fund (FWF) through project number I 6427-N (as part of the SFB/TRR 352) is gratefully acknowledged.","publication_identifier":{"issn":["0022-1236"],"eissn":["1096--0783"]},"_id":"14931","article_processing_charge":"Yes (in subscription journal)","oa":1,"volume":286,"date_updated":"2024-02-05T12:53:21Z","arxiv":1,"title":"Ground state energy of the dilute spin-polarized Fermi gas: Upper bound via cluster expansion","external_id":{"arxiv":["2301.04894"]},"ec_funded":1,"doi":"10.1016/j.jfa.2024.110320","year":"2024","article_number":"110320","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1016/j.jfa.2024.110320"}],"status":"public","intvolume":"       286","type":"journal_article","day":"24","publication":"Journal of Functional Analysis","issue":"7","language":[{"iso":"eng"}],"scopus_import":"1","publisher":"Elsevier","article_type":"original","date_published":"2024-01-24T00:00:00Z","month":"01","date_created":"2024-02-04T23:00:53Z","department":[{"_id":"RoSe"}]},{"publication_status":"published","citation":{"short":"A. Agresti, A. Hussein, Journal of Functional Analysis 285 (2023).","ista":"Agresti A, Hussein A. 2023. Maximal Lp-regularity and H∞-calculus for block operator matrices and applications. Journal of Functional Analysis. 285(11), 110146.","mla":"Agresti, Antonio, and Amru Hussein. “Maximal Lp-Regularity and H∞-Calculus for Block Operator Matrices and Applications.” <i>Journal of Functional Analysis</i>, vol. 285, no. 11, 110146, Elsevier, 2023, doi:<a href=\"https://doi.org/10.1016/j.jfa.2023.110146\">10.1016/j.jfa.2023.110146</a>.","ama":"Agresti A, Hussein A. Maximal Lp-regularity and H∞-calculus for block operator matrices and applications. <i>Journal of Functional Analysis</i>. 2023;285(11). doi:<a href=\"https://doi.org/10.1016/j.jfa.2023.110146\">10.1016/j.jfa.2023.110146</a>","chicago":"Agresti, Antonio, and Amru Hussein. “Maximal Lp-Regularity and H∞-Calculus for Block Operator Matrices and Applications.” <i>Journal of Functional Analysis</i>. Elsevier, 2023. <a href=\"https://doi.org/10.1016/j.jfa.2023.110146\">https://doi.org/10.1016/j.jfa.2023.110146</a>.","apa":"Agresti, A., &#38; Hussein, A. (2023). Maximal Lp-regularity and H∞-calculus for block operator matrices and applications. <i>Journal of Functional Analysis</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jfa.2023.110146\">https://doi.org/10.1016/j.jfa.2023.110146</a>","ieee":"A. Agresti and A. Hussein, “Maximal Lp-regularity and H∞-calculus for block operator matrices and applications,” <i>Journal of Functional Analysis</i>, vol. 285, no. 11. Elsevier, 2023."},"abstract":[{"lang":"eng","text":"Many coupled evolution equations can be described via 2×2-block operator matrices of the form A=[ \r\nA\tB\r\nC\tD\r\n ] in a product space X=X1×X2 with possibly unbounded entries. Here, the case of diagonally dominant block operator matrices is considered, that is, the case where the full operator A can be seen as a relatively bounded perturbation of its diagonal part with D(A)=D(A)×D(D) though with possibly large relative bound. For such operators the properties of sectoriality, R-sectoriality and the boundedness of the H∞-calculus are studied, and for these properties perturbation results for possibly large but structured perturbations are derived. Thereby, the time dependent parabolic problem associated with A can be analyzed in maximal Lpt\r\n-regularity spaces, and this is applied to a wide range of problems such as different theories for liquid crystals, an artificial Stokes system, strongly damped wave and plate equations, and a Keller-Segel model."}],"author":[{"full_name":"Agresti, Antonio","last_name":"Agresti","orcid":"0000-0002-9573-2962","first_name":"Antonio","id":"673cd0cc-9b9a-11eb-b144-88f30e1fbb72"},{"first_name":"Amru","last_name":"Hussein","full_name":"Hussein, Amru"}],"keyword":["Analysis"],"arxiv":1,"volume":285,"date_updated":"2024-01-10T11:24:56Z","oa":1,"article_processing_charge":"Yes (in subscription journal)","_id":"14772","publication_identifier":{"issn":["0022-1236"]},"acknowledgement":"We would like to thank Tim Binz, Emiel Lorist and Mark Veraar for valuable discussions. We also thank the anonymous referees for their helpful comments and suggestions, and for the very accurate reading of the manuscript.\r\nThe first author has been supported partially by the Nachwuchsring – Network for the promotion of young scientists – at TU Kaiserslautern. Both authors have been supported by MathApp – Mathematics Applied to Real-World Problems - part of the Research Initiative of the Federal State of Rhineland-Palatinate, Germany.","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1","oa_version":"Published Version","year":"2023","doi":"10.1016/j.jfa.2023.110146","title":"Maximal Lp-regularity and H∞-calculus for block operator matrices and applications","external_id":{"arxiv":["2108.01962"],"isi":["001081809000001"]},"tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_number":"110146","isi":1,"ddc":["510"],"day":"01","type":"journal_article","intvolume":"       285","status":"public","issue":"11","publication":"Journal of Functional Analysis","file_date_updated":"2024-01-10T11:23:57Z","month":"12","article_type":"original","date_published":"2023-12-01T00:00:00Z","publisher":"Elsevier","scopus_import":"1","language":[{"iso":"eng"}],"has_accepted_license":"1","department":[{"_id":"JuFi"}],"date_created":"2024-01-10T09:15:18Z","file":[{"checksum":"eda98ca2aa73da91bd074baed34c2b3c","date_created":"2024-01-10T11:23:57Z","file_size":1120592,"file_name":"2023_JourFunctionalAnalysis_Agresti.pdf","access_level":"open_access","date_updated":"2024-01-10T11:23:57Z","success":1,"file_id":"14789","creator":"dernst","relation":"main_file","content_type":"application/pdf"}]},{"publisher":"Elsevier","scopus_import":"1","language":[{"iso":"eng"}],"month":"11","date_published":"2023-11-15T00:00:00Z","article_type":"original","file":[{"checksum":"28e424ad91be6219e9d321054ce3a412","date_created":"2024-01-30T14:15:16Z","file_size":232934,"file_name":"2023_JourFunctionalAnalysis_Seiringer.pdf","access_level":"open_access","date_updated":"2024-01-30T14:15:16Z","success":1,"creator":"dernst","file_id":"14915","relation":"main_file","content_type":"application/pdf"}],"date_created":"2023-09-03T22:01:14Z","has_accepted_license":"1","department":[{"_id":"RoSe"}],"intvolume":"       285","status":"public","day":"15","type":"journal_article","issue":"10","publication":"Journal of Functional Analysis","file_date_updated":"2024-01-30T14:15:16Z","title":"A simple approach to Lieb-Thirring type inequalities","external_id":{"isi":["001071552300001"],"arxiv":["2303.04504"]},"year":"2023","doi":"10.1016/j.jfa.2023.110129","ddc":["510"],"tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_number":"110129","isi":1,"abstract":[{"text":"In [10] Nam proved a Lieb–Thirring Inequality for the kinetic energy of a fermionic quantum system, with almost optimal (semi-classical) constant and a gradient correction term. We present a stronger version of this inequality, with a much simplified proof. As a corollary we obtain a simple proof of the original Lieb–Thirring inequality.","lang":"eng"}],"author":[{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","last_name":"Seiringer","full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521"},{"first_name":"Jan Philip","full_name":"Solovej, Jan Philip","last_name":"Solovej"}],"publication_status":"published","citation":{"mla":"Seiringer, Robert, and Jan Philip Solovej. “A Simple Approach to Lieb-Thirring Type Inequalities.” <i>Journal of Functional Analysis</i>, vol. 285, no. 10, 110129, Elsevier, 2023, doi:<a href=\"https://doi.org/10.1016/j.jfa.2023.110129\">10.1016/j.jfa.2023.110129</a>.","ama":"Seiringer R, Solovej JP. A simple approach to Lieb-Thirring type inequalities. <i>Journal of Functional Analysis</i>. 2023;285(10). doi:<a href=\"https://doi.org/10.1016/j.jfa.2023.110129\">10.1016/j.jfa.2023.110129</a>","short":"R. Seiringer, J.P. Solovej, Journal of Functional Analysis 285 (2023).","ista":"Seiringer R, Solovej JP. 2023. A simple approach to Lieb-Thirring type inequalities. Journal of Functional Analysis. 285(10), 110129.","apa":"Seiringer, R., &#38; Solovej, J. P. (2023). A simple approach to Lieb-Thirring type inequalities. <i>Journal of Functional Analysis</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jfa.2023.110129\">https://doi.org/10.1016/j.jfa.2023.110129</a>","ieee":"R. Seiringer and J. P. Solovej, “A simple approach to Lieb-Thirring type inequalities,” <i>Journal of Functional Analysis</i>, vol. 285, no. 10. Elsevier, 2023.","chicago":"Seiringer, Robert, and Jan Philip Solovej. “A Simple Approach to Lieb-Thirring Type Inequalities.” <i>Journal of Functional Analysis</i>. Elsevier, 2023. <a href=\"https://doi.org/10.1016/j.jfa.2023.110129\">https://doi.org/10.1016/j.jfa.2023.110129</a>."},"_id":"14254","publication_identifier":{"eissn":["1096-0783"],"issn":["0022-1236"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","acknowledgement":"J.P.S. thanks the Institute of Science and Technology Austria for the hospitality and support during a visit where this work was done. J.P.S. was also partially supported by the VILLUM Centre of Excellence for the Mathematics of Quantum Theory (QMATH) (grant No. 10059).","quality_controlled":"1","oa_version":"Published Version","arxiv":1,"volume":285,"date_updated":"2024-01-30T14:17:23Z","oa":1,"article_processing_charge":"Yes (via OA deal)"},{"title":"A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature","external_id":{"isi":["000990804300001"],"arxiv":["2106.11217"]},"year":"2023","doi":"10.1016/j.jfa.2023.109963","ec_funded":1,"related_material":{"record":[{"id":"9792","relation":"earlier_version","status":"public"}]},"isi":1,"article_number":"109963","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2106.11217"}],"abstract":[{"text":"This paper establishes new connections between many-body quantum systems, One-body Reduced Density Matrices Functional Theory (1RDMFT) and Optimal Transport (OT), by interpreting the problem of computing the ground-state energy of a finite-dimensional composite quantum system at positive temperature as a non-commutative entropy regularized Optimal Transport problem. We develop a new approach to fully characterize the dual-primal solutions in such non-commutative setting. The mathematical formalism is particularly relevant in quantum chemistry: numerical realizations of the many-electron ground-state energy can be computed via a non-commutative version of Sinkhorn algorithm. Our approach allows to prove convergence and robustness of this algorithm, which, to our best knowledge, were unknown even in the two marginal case. Our methods are based on a priori estimates in the dual problem, which we believe to be of independent interest. Finally, the above results are extended in 1RDMFT setting, where bosonic or fermionic symmetry conditions are enforced on the problem.","lang":"eng"}],"author":[{"id":"41A639AA-F248-11E8-B48F-1D18A9856A87","last_name":"Feliciangeli","full_name":"Feliciangeli, Dario","orcid":"0000-0003-0754-8530","first_name":"Dario"},{"last_name":"Gerolin","full_name":"Gerolin, Augusto","first_name":"Augusto"},{"full_name":"Portinale, Lorenzo","last_name":"Portinale","first_name":"Lorenzo","id":"30AD2CBC-F248-11E8-B48F-1D18A9856A87"}],"publication_status":"published","citation":{"apa":"Feliciangeli, D., Gerolin, A., &#38; Portinale, L. (2023). A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature. <i>Journal of Functional Analysis</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jfa.2023.109963\">https://doi.org/10.1016/j.jfa.2023.109963</a>","ieee":"D. Feliciangeli, A. Gerolin, and L. Portinale, “A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature,” <i>Journal of Functional Analysis</i>, vol. 285, no. 4. Elsevier, 2023.","chicago":"Feliciangeli, Dario, Augusto Gerolin, and Lorenzo Portinale. “A Non-Commutative Entropic Optimal Transport Approach to Quantum Composite Systems at Positive Temperature.” <i>Journal of Functional Analysis</i>. Elsevier, 2023. <a href=\"https://doi.org/10.1016/j.jfa.2023.109963\">https://doi.org/10.1016/j.jfa.2023.109963</a>.","mla":"Feliciangeli, Dario, et al. “A Non-Commutative Entropic Optimal Transport Approach to Quantum Composite Systems at Positive Temperature.” <i>Journal of Functional Analysis</i>, vol. 285, no. 4, 109963, Elsevier, 2023, doi:<a href=\"https://doi.org/10.1016/j.jfa.2023.109963\">10.1016/j.jfa.2023.109963</a>.","ama":"Feliciangeli D, Gerolin A, Portinale L. A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature. <i>Journal of Functional Analysis</i>. 2023;285(4). doi:<a href=\"https://doi.org/10.1016/j.jfa.2023.109963\">10.1016/j.jfa.2023.109963</a>","ista":"Feliciangeli D, Gerolin A, Portinale L. 2023. A non-commutative entropic optimal transport approach to quantum composite systems at positive temperature. Journal of Functional Analysis. 285(4), 109963.","short":"D. Feliciangeli, A. Gerolin, L. Portinale, Journal of Functional Analysis 285 (2023)."},"_id":"12911","publication_identifier":{"issn":["0022-1236"],"eissn":["1096-0783"]},"acknowledgement":"This work started when A.G. was visiting the Erwin Schrödinger Institute and then continued when D.F. and L.P visited the Theoretical Chemistry Department of the Vrije Universiteit Amsterdam. The authors thank the hospitality of both places and, especially, P. Gori-Giorgi and K. Giesbertz for fruitful discussions and literature suggestions in the early state of the project. The authors also thank J. Maas and R. Seiringer for their feedback and useful comments to a first draft of the article. Finally, we acknowledge the high quality review done by the anonymous referee of our paper, who we would like to thank for the excellent work and constructive feedback.\r\nD.F acknowledges support by the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreements No 716117 and No 694227). A.G. acknowledges funding by the HORIZON EUROPE European Research Council under H2020/MSCA-IF “OTmeetsDFT” [grant ID: 795942] as well as partial support of his research by the Canada Research Chairs Program (ID 2021-00234) and Natural Sciences and Engineering Research Council of Canada, RGPIN-2022-05207. L.P. acknowledges support by the Austrian Science Fund (FWF), grants No W1245 and No F65, and by the Deutsche Forschungsgemeinschaft (DFG) - Project number 390685813.","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","project":[{"grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"grant_number":"694227","call_identifier":"H2020","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","name":"Analysis of quantum many-body systems"},{"grant_number":" F06504","_id":"260482E2-B435-11E9-9278-68D0E5697425","name":"Taming Complexity in Partial Di erential Systems","call_identifier":"FWF"}],"oa_version":"Preprint","quality_controlled":"1","arxiv":1,"oa":1,"date_updated":"2023-11-14T13:21:01Z","volume":285,"article_processing_charge":"No","publisher":"Elsevier","scopus_import":"1","language":[{"iso":"eng"}],"month":"08","date_published":"2023-08-15T00:00:00Z","article_type":"original","date_created":"2023-05-07T22:01:02Z","department":[{"_id":"RoSe"},{"_id":"JaMa"}],"intvolume":"       285","status":"public","day":"15","type":"journal_article","issue":"4","publication":"Journal of Functional Analysis"},{"day":"15","type":"journal_article","intvolume":"       282","status":"public","issue":"8","publication":"Journal of Functional Analysis","file_date_updated":"2022-07-29T07:22:08Z","month":"04","date_published":"2022-04-15T00:00:00Z","article_type":"original","publisher":"Elsevier","scopus_import":"1","language":[{"iso":"eng"}],"has_accepted_license":"1","department":[{"_id":"LaEr"}],"file":[{"relation":"main_file","content_type":"application/pdf","creator":"dernst","file_id":"11690","success":1,"access_level":"open_access","date_updated":"2022-07-29T07:22:08Z","file_size":652573,"file_name":"2022_JourFunctionalAnalysis_Cipolloni.pdf","checksum":"b75fdad606ab507dc61109e0907d86c0","date_created":"2022-07-29T07:22:08Z"}],"date_created":"2022-02-06T23:01:30Z","publication_status":"published","citation":{"ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Thermalisation for Wigner matrices,” <i>Journal of Functional Analysis</i>, vol. 282, no. 8. Elsevier, 2022.","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2022). Thermalisation for Wigner matrices. <i>Journal of Functional Analysis</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jfa.2022.109394\">https://doi.org/10.1016/j.jfa.2022.109394</a>","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Thermalisation for Wigner Matrices.” <i>Journal of Functional Analysis</i>. Elsevier, 2022. <a href=\"https://doi.org/10.1016/j.jfa.2022.109394\">https://doi.org/10.1016/j.jfa.2022.109394</a>.","mla":"Cipolloni, Giorgio, et al. “Thermalisation for Wigner Matrices.” <i>Journal of Functional Analysis</i>, vol. 282, no. 8, 109394, Elsevier, 2022, doi:<a href=\"https://doi.org/10.1016/j.jfa.2022.109394\">10.1016/j.jfa.2022.109394</a>.","ama":"Cipolloni G, Erdös L, Schröder DJ. Thermalisation for Wigner matrices. <i>Journal of Functional Analysis</i>. 2022;282(8). doi:<a href=\"https://doi.org/10.1016/j.jfa.2022.109394\">10.1016/j.jfa.2022.109394</a>","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Thermalisation for Wigner matrices. Journal of Functional Analysis. 282(8), 109394.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Journal of Functional Analysis 282 (2022)."},"abstract":[{"lang":"eng","text":"We compute the deterministic approximation of products of Sobolev functions of large Wigner matrices W and provide an optimal error bound on their fluctuation with very high probability. This generalizes Voiculescu's seminal theorem from polynomials to general Sobolev functions, as well as from tracial quantities to individual matrix elements. Applying the result to eitW for large t, we obtain a precise decay rate for the overlaps of several deterministic matrices with temporally well separated Heisenberg time evolutions; thus we demonstrate the thermalisation effect of the unitary group generated by Wigner matrices."}],"author":[{"full_name":"Cipolloni, Giorgio","last_name":"Cipolloni","orcid":"0000-0002-4901-7992","first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","first_name":"László"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J","orcid":"0000-0002-2904-1856","last_name":"Schröder","full_name":"Schröder, Dominik J"}],"arxiv":1,"date_updated":"2023-08-02T14:12:35Z","volume":282,"oa":1,"article_processing_charge":"Yes (via OA deal)","_id":"10732","publication_identifier":{"issn":["0022-1236"],"eissn":["1096-0783"]},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","acknowledgement":"We compute the deterministic approximation of products of Sobolev functions of large Wigner matrices W and provide an optimal error bound on their fluctuation with very high probability. This generalizes Voiculescu's seminal theorem from polynomials to general Sobolev functions, as well as from tracial quantities to individual matrix elements. Applying the result to  for large t, we obtain a precise decay rate for the overlaps of several deterministic matrices with temporally well separated Heisenberg time evolutions; thus we demonstrate the thermalisation effect of the unitary group generated by Wigner matrices.","oa_version":"Published Version","quality_controlled":"1","year":"2022","doi":"10.1016/j.jfa.2022.109394","title":"Thermalisation for Wigner matrices","external_id":{"isi":["000781239100004"],"arxiv":["2102.09975"]},"tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"isi":1,"article_number":"109394","ddc":["500"]},{"publication":"Journal of Functional Analysis","issue":"12","file_date_updated":"2022-08-02T10:37:55Z","intvolume":"       282","status":"public","day":"15","type":"journal_article","file":[{"success":1,"content_type":"application/pdf","relation":"main_file","file_id":"11720","creator":"dernst","file_name":"2022_JourFunctionalAnalysis_Roos.pdf","file_size":631391,"date_created":"2022-08-02T10:37:55Z","checksum":"63efcefaa1f2717244ef5407bd564426","date_updated":"2022-08-02T10:37:55Z","access_level":"open_access"}],"date_created":"2022-03-16T08:41:53Z","has_accepted_license":"1","department":[{"_id":"GradSch"},{"_id":"RoSe"}],"scopus_import":"1","publisher":"Elsevier","language":[{"iso":"eng"}],"month":"06","article_type":"original","date_published":"2022-06-15T00:00:00Z","publication_identifier":{"issn":["0022-1236"]},"_id":"10850","project":[{"grant_number":"694227","call_identifier":"H2020","name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"}],"oa_version":"Published Version","quality_controlled":"1","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","acknowledgement":"We thank Rupert Frank for contributing Appendix B. Funding from the European Union's Horizon 2020 research and innovation programme under the ERC grant agreement No. 694227 is gratefully acknowledged.","arxiv":1,"article_processing_charge":"Yes (via OA deal)","oa":1,"volume":282,"date_updated":"2023-10-27T10:37:29Z","abstract":[{"text":"We study two interacting quantum particles forming a bound state in d-dimensional free\r\nspace, and constrain the particles in k directions to (0, ∞)k ×Rd−k, with Neumann boundary\r\nconditions. First, we prove that the ground state energy strictly decreases upon going from k\r\nto k+1. This shows that the particles stick to the corner where all boundary planes intersect.\r\nSecond, we show that for all k the resulting Hamiltonian, after removing the free part of the\r\nkinetic energy, has only finitely many eigenvalues below the essential spectrum. This paper\r\ngeneralizes the work of Egger, Kerner and Pankrashkin (J. Spectr. Theory 10(4):1413–1444,\r\n2020) to dimensions d > 1.","lang":"eng"}],"keyword":["Analysis"],"author":[{"id":"5DA90512-D80F-11E9-8994-2E2EE6697425","first_name":"Barbara","orcid":"0000-0002-9071-5880","last_name":"Roos","full_name":"Roos, Barbara"},{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","full_name":"Seiringer, Robert","last_name":"Seiringer","orcid":"0000-0002-6781-0521"}],"citation":{"chicago":"Roos, Barbara, and Robert Seiringer. “Two-Particle Bound States at Interfaces and Corners.” <i>Journal of Functional Analysis</i>. Elsevier, 2022. <a href=\"https://doi.org/10.1016/j.jfa.2022.109455\">https://doi.org/10.1016/j.jfa.2022.109455</a>.","ieee":"B. Roos and R. Seiringer, “Two-particle bound states at interfaces and corners,” <i>Journal of Functional Analysis</i>, vol. 282, no. 12. Elsevier, 2022.","apa":"Roos, B., &#38; Seiringer, R. (2022). Two-particle bound states at interfaces and corners. <i>Journal of Functional Analysis</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jfa.2022.109455\">https://doi.org/10.1016/j.jfa.2022.109455</a>","ista":"Roos B, Seiringer R. 2022. Two-particle bound states at interfaces and corners. Journal of Functional Analysis. 282(12), 109455.","short":"B. Roos, R. Seiringer, Journal of Functional Analysis 282 (2022).","mla":"Roos, Barbara, and Robert Seiringer. “Two-Particle Bound States at Interfaces and Corners.” <i>Journal of Functional Analysis</i>, vol. 282, no. 12, 109455, Elsevier, 2022, doi:<a href=\"https://doi.org/10.1016/j.jfa.2022.109455\">10.1016/j.jfa.2022.109455</a>.","ama":"Roos B, Seiringer R. Two-particle bound states at interfaces and corners. <i>Journal of Functional Analysis</i>. 2022;282(12). doi:<a href=\"https://doi.org/10.1016/j.jfa.2022.109455\">10.1016/j.jfa.2022.109455</a>"},"publication_status":"published","related_material":{"record":[{"relation":"dissertation_contains","id":"14374","status":"public"}]},"ddc":["510"],"tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_number":"109455","isi":1,"external_id":{"isi":["000795160200009"],"arxiv":["2105.04874"]},"title":"Two-particle bound states at interfaces and corners","doi":"10.1016/j.jfa.2022.109455","year":"2022","ec_funded":1},{"title":"Functional John ellipsoids","external_id":{"isi":["000781371300008"],"arxiv":["2006.09934"]},"year":"2022","doi":"10.1016/j.jfa.2022.109441","ddc":["510"],"isi":1,"article_number":"109441","tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"author":[{"id":"87744F66-5C6F-11EA-AFE0-D16B3DDC885E","full_name":"Ivanov, Grigory","last_name":"Ivanov","first_name":"Grigory"},{"first_name":"Márton","last_name":"Naszódi","full_name":"Naszódi, Márton"}],"abstract":[{"lang":"eng","text":"We introduce a new way of representing logarithmically concave functions on Rd. It allows us to extend the notion of the largest volume ellipsoid contained in a convex body to the setting of logarithmically concave functions as follows. For every s>0, we define a class of non-negative functions on Rd derived from ellipsoids in Rd+1. For any log-concave function f on Rd , and any fixed s>0, we consider functions belonging to this class, and find the one with the largest integral under the condition that it is pointwise less than or equal to f, and we call it the John s-function of f. After establishing existence and uniqueness, we give a characterization of this function similar to the one given by John in his fundamental theorem. We find that John s-functions converge to characteristic functions of ellipsoids as s tends to zero and to Gaussian densities as s tends to infinity.\r\nAs an application, we prove a quantitative Helly type result: the integral of the pointwise minimum of any family of log-concave functions is at least a constant cd multiple of the integral of the pointwise minimum of a properly chosen subfamily of size 3d+2, where cd depends only on d."}],"citation":{"short":"G. Ivanov, M. Naszódi, Journal of Functional Analysis 282 (2022).","ista":"Ivanov G, Naszódi M. 2022. Functional John ellipsoids. Journal of Functional Analysis. 282(11), 109441.","ama":"Ivanov G, Naszódi M. Functional John ellipsoids. <i>Journal of Functional Analysis</i>. 2022;282(11). doi:<a href=\"https://doi.org/10.1016/j.jfa.2022.109441\">10.1016/j.jfa.2022.109441</a>","mla":"Ivanov, Grigory, and Márton Naszódi. “Functional John Ellipsoids.” <i>Journal of Functional Analysis</i>, vol. 282, no. 11, 109441, Elsevier, 2022, doi:<a href=\"https://doi.org/10.1016/j.jfa.2022.109441\">10.1016/j.jfa.2022.109441</a>.","chicago":"Ivanov, Grigory, and Márton Naszódi. “Functional John Ellipsoids.” <i>Journal of Functional Analysis</i>. Elsevier, 2022. <a href=\"https://doi.org/10.1016/j.jfa.2022.109441\">https://doi.org/10.1016/j.jfa.2022.109441</a>.","apa":"Ivanov, G., &#38; Naszódi, M. (2022). Functional John ellipsoids. <i>Journal of Functional Analysis</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jfa.2022.109441\">https://doi.org/10.1016/j.jfa.2022.109441</a>","ieee":"G. Ivanov and M. Naszódi, “Functional John ellipsoids,” <i>Journal of Functional Analysis</i>, vol. 282, no. 11. Elsevier, 2022."},"publication_status":"published","oa_version":"Published Version","quality_controlled":"1","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","acknowledgement":"G.I. was supported by the Ministry of Education and Science of the Russian Federation in the framework of MegaGrant no 075-15-2019-1926. M.N. was supported by the National Research, Development and Innovation Fund (NRDI) grants K119670 and KKP-133864 as well as the Bolyai Scholarship of the Hungarian Academy of Sciences and the New National Excellence Programme and the TKP2020-NKA-06 program provided by the NRDI. ","publication_identifier":{"issn":["0022-1236"],"eissn":["1096-0783"]},"_id":"10887","article_processing_charge":"Yes (via OA deal)","date_updated":"2023-08-02T14:51:11Z","oa":1,"volume":282,"arxiv":1,"language":[{"iso":"eng"}],"scopus_import":"1","publisher":"Elsevier","date_published":"2022-06-01T00:00:00Z","article_type":"original","month":"06","date_created":"2022-03-20T23:01:38Z","file":[{"checksum":"1cf185e264e04c87cb1ce67a00db88ab","date_created":"2022-08-02T10:40:48Z","file_size":734482,"file_name":"2022_JourFunctionalAnalysis_Ivanov.pdf","access_level":"open_access","date_updated":"2022-08-02T10:40:48Z","success":1,"file_id":"11721","creator":"dernst","relation":"main_file","content_type":"application/pdf"}],"department":[{"_id":"UlWa"}],"has_accepted_license":"1","status":"public","intvolume":"       282","type":"journal_article","day":"01","file_date_updated":"2022-08-02T10:40:48Z","publication":"Journal of Functional Analysis","issue":"11"},{"publication_status":"published","citation":{"apa":"Brooks, M., &#38; Di Gesù, G. (2021). Sharp tunneling estimates for a double-well model in infinite dimension. <i>Journal of Functional Analysis</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jfa.2021.109029\">https://doi.org/10.1016/j.jfa.2021.109029</a>","ieee":"M. Brooks and G. Di Gesù, “Sharp tunneling estimates for a double-well model in infinite dimension,” <i>Journal of Functional Analysis</i>, vol. 281, no. 3. Elsevier, 2021.","chicago":"Brooks, Morris, and Giacomo Di Gesù. “Sharp Tunneling Estimates for a Double-Well Model in Infinite Dimension.” <i>Journal of Functional Analysis</i>. Elsevier, 2021. <a href=\"https://doi.org/10.1016/j.jfa.2021.109029\">https://doi.org/10.1016/j.jfa.2021.109029</a>.","ama":"Brooks M, Di Gesù G. Sharp tunneling estimates for a double-well model in infinite dimension. <i>Journal of Functional Analysis</i>. 2021;281(3). doi:<a href=\"https://doi.org/10.1016/j.jfa.2021.109029\">10.1016/j.jfa.2021.109029</a>","mla":"Brooks, Morris, and Giacomo Di Gesù. “Sharp Tunneling Estimates for a Double-Well Model in Infinite Dimension.” <i>Journal of Functional Analysis</i>, vol. 281, no. 3, 109029, Elsevier, 2021, doi:<a href=\"https://doi.org/10.1016/j.jfa.2021.109029\">10.1016/j.jfa.2021.109029</a>.","ista":"Brooks M, Di Gesù G. 2021. Sharp tunneling estimates for a double-well model in infinite dimension. Journal of Functional Analysis. 281(3), 109029.","short":"M. Brooks, G. Di Gesù, Journal of Functional Analysis 281 (2021)."},"author":[{"id":"B7ECF9FC-AA38-11E9-AC9A-0930E6697425","first_name":"Morris","orcid":"0000-0002-6249-0928","full_name":"Brooks, Morris","last_name":"Brooks"},{"last_name":"Di Gesù","full_name":"Di Gesù, Giacomo","first_name":"Giacomo"}],"abstract":[{"text":"We consider the stochastic quantization of a quartic double-well energy functional in the semiclassical regime and derive optimal asymptotics for the exponentially small splitting of the ground state energy. Our result provides an infinite-dimensional version of some sharp tunneling estimates known in finite dimensions for semiclassical Witten Laplacians in degree zero. From a stochastic point of view it proves that the L2 spectral gap of the stochastic one-dimensional Allen-Cahn equation in finite volume satisfies a Kramers-type formula in the limit of vanishing noise. We work with finite-dimensional lattice approximations and establish semiclassical estimates which are uniform in the dimension. Our key estimate shows that the constant separating the two exponentially small eigenvalues from the rest of the spectrum can be taken independently of the dimension.","lang":"eng"}],"volume":281,"date_updated":"2023-08-08T13:15:11Z","oa":1,"article_processing_charge":"No","arxiv":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","acknowledgement":"GDG gratefully acknowledges the financial support of HIM Bonn in the framework of the 2019 Junior Trimester Programs “Kinetic Theory” and “Randomness, PDEs and Nonlinear Fluctuations” and the hospitality at the University of Rome La Sapienza during his frequent visits.","oa_version":"Preprint","quality_controlled":"1","_id":"9348","publication_identifier":{"issn":["0022-1236"],"eissn":["1096-0783"]},"doi":"10.1016/j.jfa.2021.109029","year":"2021","external_id":{"arxiv":["1911.03187"],"isi":["000644702800005"]},"title":"Sharp tunneling estimates for a double-well model in infinite dimension","isi":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1911.03187"}],"article_number":"109029","type":"journal_article","day":"07","status":"public","intvolume":"       281","issue":"3","publication":"Journal of Functional Analysis","article_type":"original","date_published":"2021-04-07T00:00:00Z","month":"04","language":[{"iso":"eng"}],"publisher":"Elsevier","scopus_import":"1","department":[{"_id":"RoSe"}],"date_created":"2021-04-25T22:01:29Z"},{"external_id":{"arxiv":["2009.00992"],"isi":["000656508600008"]},"title":"Semiclassical approximation and critical temperature shift for weakly interacting trapped bosons","year":"2021","doi":"10.1016/j.jfa.2021.109096","ec_funded":1,"article_number":"109096","isi":1,"main_file_link":[{"url":"https://arxiv.org/abs/2009.00992","open_access":"1"}],"abstract":[{"lang":"eng","text":"We consider a system of N trapped bosons with repulsive interactions in a combined semiclassical mean-field limit at positive temperature. We show that the free energy is well approximated by the minimum of the Hartree free energy functional – a natural extension of the Hartree energy functional to positive temperatures. The Hartree free energy functional converges in the same limit to a semiclassical free energy functional, and we show that the system displays Bose–Einstein condensation if and only if it occurs in the semiclassical free energy functional. This allows us to show that for weak coupling the critical temperature decreases due to the repulsive interactions."}],"author":[{"first_name":"Andreas","full_name":"Deuchert, Andreas","last_name":"Deuchert"},{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","orcid":"0000-0002-6781-0521","full_name":"Seiringer, Robert","last_name":"Seiringer"}],"citation":{"chicago":"Deuchert, Andreas, and Robert Seiringer. “Semiclassical Approximation and Critical Temperature Shift for Weakly Interacting Trapped Bosons.” <i>Journal of Functional Analysis</i>. Elsevier, 2021. <a href=\"https://doi.org/10.1016/j.jfa.2021.109096\">https://doi.org/10.1016/j.jfa.2021.109096</a>.","apa":"Deuchert, A., &#38; Seiringer, R. (2021). Semiclassical approximation and critical temperature shift for weakly interacting trapped bosons. <i>Journal of Functional Analysis</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jfa.2021.109096\">https://doi.org/10.1016/j.jfa.2021.109096</a>","ieee":"A. Deuchert and R. Seiringer, “Semiclassical approximation and critical temperature shift for weakly interacting trapped bosons,” <i>Journal of Functional Analysis</i>, vol. 281, no. 6. Elsevier, 2021.","short":"A. Deuchert, R. Seiringer, Journal of Functional Analysis 281 (2021).","ista":"Deuchert A, Seiringer R. 2021. Semiclassical approximation and critical temperature shift for weakly interacting trapped bosons. Journal of Functional Analysis. 281(6), 109096.","mla":"Deuchert, Andreas, and Robert Seiringer. “Semiclassical Approximation and Critical Temperature Shift for Weakly Interacting Trapped Bosons.” <i>Journal of Functional Analysis</i>, vol. 281, no. 6, 109096, Elsevier, 2021, doi:<a href=\"https://doi.org/10.1016/j.jfa.2021.109096\">10.1016/j.jfa.2021.109096</a>.","ama":"Deuchert A, Seiringer R. Semiclassical approximation and critical temperature shift for weakly interacting trapped bosons. <i>Journal of Functional Analysis</i>. 2021;281(6). doi:<a href=\"https://doi.org/10.1016/j.jfa.2021.109096\">10.1016/j.jfa.2021.109096</a>"},"publication_status":"published","publication_identifier":{"eissn":["1096-0783"],"issn":["0022-1236"]},"_id":"9462","quality_controlled":"1","project":[{"grant_number":"694227","call_identifier":"H2020","name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"}],"oa_version":"Preprint","acknowledgement":"Funding from the European Union's Horizon 2020 research and innovation programme under the ERC grant agreement No 694227 (R.S.) and under the Marie Sklodowska-Curie grant agreement No 836146 (A.D.) is gratefully acknowledged. A.D. acknowledges support of the Swiss National Science Foundation through the Ambizione grant PZ00P2 185851.","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","arxiv":1,"article_processing_charge":"No","volume":281,"date_updated":"2023-08-08T13:56:27Z","oa":1,"scopus_import":"1","publisher":"Elsevier","language":[{"iso":"eng"}],"month":"09","date_published":"2021-09-15T00:00:00Z","article_type":"original","date_created":"2021-06-06T22:01:28Z","department":[{"_id":"RoSe"}],"intvolume":"       281","status":"public","day":"15","type":"journal_article","publication":"Journal of Functional Analysis","issue":"6"},{"arxiv":1,"article_processing_charge":"No","oa":1,"date_updated":"2023-08-14T07:05:44Z","volume":281,"publication_identifier":{"issn":["0022-1236"],"eissn":["1096-0783"]},"_id":"10070","quality_controlled":"1","oa_version":"Preprint","project":[{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504"},{"grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425","name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020"}],"acknowledgement":"The authors are grateful to Professor Kazuhiro Kuwae for kindly providing a copy of [49]. They are also grateful to Dr. Bang-Xian Han for helpful discussions on the Sobolev-to-Lipschitz property on metric measure spaces. They wish to express their deepest gratitude to an anonymous Reviewer, whose punctual remarks and comments greatly improved the accessibility and overall quality of the initial submission. This work was completed while L.D.S. was a member of the Institut für Angewandte Mathematik of the University of Bonn. He acknowledges funding of his position at that time by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through the Sonderforschungsbereich (Sfb, Collaborative Research Center) 1060 - project number 211504053. He also acknowledges funding of his current position by the Austrian Science Fund (FWF) grant F65, and by the European Research Council (ERC, grant No. 716117, awarded to Prof. Dr. Jan Maas). K.S. gratefully acknowledges funding by: the JSPS Overseas Research Fellowships, Grant Nr. 290142; World Premier International Research Center Initiative (WPI), MEXT, Japan; and JSPS Grant-in-Aid for Scientific Research on Innovative Areas “Discrete Geometric Analysis for Materials Design”, Grant Number 17H06465.","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"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.","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>","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>.","mla":"Dello Schiavo, Lorenzo, and Kohei Suzuki. “Rademacher-Type Theorems and Sobolev-to-Lipschitz Properties for Strongly Local Dirichlet Spaces.” <i>Journal of Functional Analysis</i>, vol. 281, no. 11, 109234, Elsevier, 2021, doi:<a href=\"https://doi.org/10.1016/j.jfa.2021.109234\">10.1016/j.jfa.2021.109234</a>.","ama":"Dello Schiavo L, Suzuki K. Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local Dirichlet spaces. <i>Journal of Functional Analysis</i>. 2021;281(11). doi:<a href=\"https://doi.org/10.1016/j.jfa.2021.109234\">10.1016/j.jfa.2021.109234</a>","short":"L. Dello Schiavo, K. Suzuki, Journal of Functional Analysis 281 (2021).","ista":"Dello Schiavo L, Suzuki K. 2021. Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local Dirichlet spaces. Journal of Functional Analysis. 281(11), 109234."},"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"}],"author":[{"id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","full_name":"Dello Schiavo, Lorenzo","last_name":"Dello Schiavo","orcid":"0000-0002-9881-6870","first_name":"Lorenzo"},{"last_name":"Suzuki","full_name":"Suzuki, Kohei","first_name":"Kohei"}],"isi":1,"article_number":"109234","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2008.01492"}],"doi":"10.1016/j.jfa.2021.109234","year":"2021","ec_funded":1,"title":"Rademacher-type theorems and Sobolev-to-Lipschitz properties for strongly local Dirichlet spaces","external_id":{"isi":["000703896600005"],"arxiv":["2008.01492"]},"publication":"Journal of Functional Analysis","issue":"11","day":"15","type":"journal_article","intvolume":"       281","status":"public","department":[{"_id":"JaMa"}],"date_created":"2021-10-03T22:01:21Z","month":"09","date_published":"2021-09-15T00:00:00Z","article_type":"original","scopus_import":"1","publisher":"Elsevier","language":[{"iso":"eng"}]},{"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1708.01597"}],"isi":1,"article_number":"108639","external_id":{"isi":["000559623200009"],"arxiv":["1708.01597"]},"title":"Spectral rigidity for addition of random matrices at the regular edge","ec_funded":1,"year":"2020","doi":"10.1016/j.jfa.2020.108639","oa_version":"Preprint","project":[{"grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7"}],"quality_controlled":"1","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","acknowledgement":"Partially supported by ERC Advanced Grant RANMAT No. 338804.","publication_identifier":{"issn":["0022-1236"]},"_id":"10862","article_processing_charge":"No","volume":279,"oa":1,"date_updated":"2023-08-24T14:08:42Z","arxiv":1,"author":[{"id":"442E6A6C-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-3036-1475","last_name":"Bao","full_name":"Bao, Zhigang","first_name":"Zhigang"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","orcid":"0000-0001-5366-9603","last_name":"Erdös","full_name":"Erdös, László"},{"first_name":"Kevin","last_name":"Schnelli","full_name":"Schnelli, Kevin"}],"keyword":["Analysis"],"abstract":[{"text":"We consider the sum of two large Hermitian matrices A and B with a Haar unitary conjugation bringing them into a general relative position. We prove that the eigenvalue density on the scale slightly above the local eigenvalue spacing is asymptotically given by the free additive convolution of the laws of A and B as the dimension of the matrix increases. This implies optimal rigidity of the eigenvalues and optimal rate of convergence in Voiculescu's theorem. Our previous works [4], [5] established these results in the bulk spectrum, the current paper completely settles the problem at the spectral edges provided they have the typical square-root behavior. The key element of our proof is to compensate the deterioration of the stability of the subordination equations by sharp error estimates that properly account for the local density near the edge. Our results also hold if the Haar unitary matrix is replaced by the Haar orthogonal matrix.","lang":"eng"}],"citation":{"chicago":"Bao, Zhigang, László Erdös, and Kevin Schnelli. “Spectral Rigidity for Addition of Random Matrices at the Regular Edge.” <i>Journal of Functional Analysis</i>. Elsevier, 2020. <a href=\"https://doi.org/10.1016/j.jfa.2020.108639\">https://doi.org/10.1016/j.jfa.2020.108639</a>.","apa":"Bao, Z., Erdös, L., &#38; Schnelli, K. (2020). Spectral rigidity for addition of random matrices at the regular edge. <i>Journal of Functional Analysis</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jfa.2020.108639\">https://doi.org/10.1016/j.jfa.2020.108639</a>","ieee":"Z. Bao, L. Erdös, and K. Schnelli, “Spectral rigidity for addition of random matrices at the regular edge,” <i>Journal of Functional Analysis</i>, vol. 279, no. 7. Elsevier, 2020.","ista":"Bao Z, Erdös L, Schnelli K. 2020. Spectral rigidity for addition of random matrices at the regular edge. Journal of Functional Analysis. 279(7), 108639.","short":"Z. Bao, L. Erdös, K. Schnelli, Journal of Functional Analysis 279 (2020).","mla":"Bao, Zhigang, et al. “Spectral Rigidity for Addition of Random Matrices at the Regular Edge.” <i>Journal of Functional Analysis</i>, vol. 279, no. 7, 108639, Elsevier, 2020, doi:<a href=\"https://doi.org/10.1016/j.jfa.2020.108639\">10.1016/j.jfa.2020.108639</a>.","ama":"Bao Z, Erdös L, Schnelli K. Spectral rigidity for addition of random matrices at the regular edge. <i>Journal of Functional Analysis</i>. 2020;279(7). doi:<a href=\"https://doi.org/10.1016/j.jfa.2020.108639\">10.1016/j.jfa.2020.108639</a>"},"publication_status":"published","date_created":"2022-03-18T10:18:59Z","department":[{"_id":"LaEr"}],"language":[{"iso":"eng"}],"scopus_import":"1","publisher":"Elsevier","article_type":"original","date_published":"2020-10-15T00:00:00Z","month":"10","publication":"Journal of Functional Analysis","issue":"7","status":"public","intvolume":"       279","type":"journal_article","day":"15"},{"type":"journal_article","day":"01","citation":{"chicago":"Bourgain, Jean, and Vadim Kaloshin. “On Diffusion in High-Dimensional Hamiltonian Systems.” <i>Journal of Functional Analysis</i>. Elsevier, 2005. <a href=\"https://doi.org/10.1016/j.jfa.2004.09.006\">https://doi.org/10.1016/j.jfa.2004.09.006</a>.","ieee":"J. Bourgain and V. Kaloshin, “On diffusion in high-dimensional Hamiltonian systems,” <i>Journal of Functional Analysis</i>, vol. 229, no. 1. Elsevier, pp. 1–61, 2005.","apa":"Bourgain, J., &#38; Kaloshin, V. (2005). On diffusion in high-dimensional Hamiltonian systems. <i>Journal of Functional Analysis</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jfa.2004.09.006\">https://doi.org/10.1016/j.jfa.2004.09.006</a>","ista":"Bourgain J, Kaloshin V. 2005. On diffusion in high-dimensional Hamiltonian systems. Journal of Functional Analysis. 229(1), 1–61.","short":"J. Bourgain, V. Kaloshin, Journal of Functional Analysis 229 (2005) 1–61.","mla":"Bourgain, Jean, and Vadim Kaloshin. “On Diffusion in High-Dimensional Hamiltonian Systems.” <i>Journal of Functional Analysis</i>, vol. 229, no. 1, Elsevier, 2005, pp. 1–61, doi:<a href=\"https://doi.org/10.1016/j.jfa.2004.09.006\">10.1016/j.jfa.2004.09.006</a>.","ama":"Bourgain J, Kaloshin V. On diffusion in high-dimensional Hamiltonian systems. <i>Journal of Functional Analysis</i>. 2005;229(1):1-61. doi:<a href=\"https://doi.org/10.1016/j.jfa.2004.09.006\">10.1016/j.jfa.2004.09.006</a>"},"publication_status":"published","status":"public","author":[{"last_name":"Bourgain","full_name":"Bourgain, Jean","first_name":"Jean"},{"first_name":"Vadim","last_name":"Kaloshin","full_name":"Kaloshin, Vadim","orcid":"0000-0002-6051-2628","id":"FE553552-CDE8-11E9-B324-C0EBE5697425"}],"keyword":["Analysis"],"abstract":[{"lang":"eng","text":"The purpose of this paper is to construct examples of diffusion for E-Hamiltonian perturbations\r\nof completely integrable Hamiltonian systems in 2d-dimensional phase space, with d large.\r\nIn the first part of the paper, simple and explicit examples are constructed illustrating absence\r\nof ‘long-time’ stability for size E Hamiltonian perturbations of quasi-convex integrable systems\r\nalready when the dimension 2d of phase space becomes as large as log 1/E . We first produce\r\nthe example in Gevrey class and then a real analytic one, with some additional work.\r\nIn the second part, we consider again E-Hamiltonian perturbations of completely integrable\r\nHamiltonian system in 2d-dimensional space with E-small but not too small, |E| > exp(−d), with\r\nd the number of degrees of freedom assumed large. It is shown that for a class of analytic\r\ntime-periodic perturbations, there exist linearly diffusing trajectories. The underlying idea for\r\nboth examples is similar and consists in coupling a fixed degree of freedom with a large\r\nnumber of them. The procedure and analytical details are however significantly different. As\r\nmentioned, the construction in Part I is totally elementary while Part II is more involved, relying\r\nin particular on the theory of normally hyperbolic invariant manifolds, methods of generating\r\nfunctions, Aubry–Mather theory, and Mather’s variational methods."}],"intvolume":"       229","page":"1-61","article_processing_charge":"No","date_updated":"2021-01-12T08:19:49Z","volume":229,"publication":"Journal of Functional Analysis","issue":"1","oa_version":"None","quality_controlled":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","extern":"1","publication_identifier":{"issn":["0022-1236"]},"_id":"8516","article_type":"original","date_published":"2005-12-01T00:00:00Z","month":"12","doi":"10.1016/j.jfa.2004.09.006","year":"2005","language":[{"iso":"eng"}],"title":"On diffusion in high-dimensional Hamiltonian systems","publisher":"Elsevier","date_created":"2020-09-18T10:49:06Z"}]