[{"type":"journal_article","publisher":"AIP Publishing","publication_status":"published","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","language":[{"iso":"eng"}],"publication":"Journal of Mathematical Physics","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2012.15238"}],"month":"01","scopus_import":"1","_id":"10600","oa_version":"Preprint","isi":1,"keyword":["mathematical physics","statistical and nonlinear physics"],"status":"public","issue":"1","date_published":"2022-01-03T00:00:00Z","fulldoi":"https://doi.org/10.1063/5.0051632","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"ec_funded":1,"quality_controlled":"1","publication_identifier":{"issn":["0022-2488"],"eissn":["1089-7658"]},"doi":"10.1063/5.0051632","author":[{"id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","last_name":"Henheik","first_name":"Sven Joscha","full_name":"Henheik, Sven Joscha","orcid":"0000-0003-1106-327X"},{"full_name":"Teufel, Stefan","last_name":"Teufel","first_name":"Stefan"}],"abstract":[{"lang":"eng","text":"We show that recent results on adiabatic theory for interacting gapped many-body systems on finite lattices remain valid in the thermodynamic limit. More precisely, we prove a generalized super-adiabatic theorem for the automorphism group describing the infinite volume dynamics on the quasi-local algebra of observables. The key assumption is the existence of a sequence of gapped finite volume Hamiltonians, which generates the same infinite volume dynamics in the thermodynamic limit. Our adiabatic theorem also holds for certain perturbations of gapped ground states that close the spectral gap (so it is also an adiabatic theorem for resonances and, in this sense, “generalized”), and it provides an adiabatic approximation to all orders in the adiabatic parameter (a property often called “super-adiabatic”). In addition to the existing results for finite lattices, we also perform a resummation of the adiabatic expansion and allow for observables that are not strictly local. Finally, as an application, we prove the validity of linear and higher order response theory for our class of perturbations for infinite systems. While we consider the result and its proof as new and interesting in itself, we also lay the foundation for the proof of an adiabatic theorem for systems with a gap only in the bulk, which will be presented in a follow-up article."}],"title":"Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap","date_updated":"2025-04-14T07:57:17Z","day":"03","volume":63,"citation":{"ista":"Henheik SJ, Teufel S. 2022. Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap. Journal of Mathematical Physics. 63(1), 011901.","apa":"Henheik, S. J., &#38; Teufel, S. (2022). Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap. <i>Journal of Mathematical Physics</i>. AIP Publishing. <a href=\"https://doi.org/10.1063/5.0051632\">https://doi.org/10.1063/5.0051632</a>","ieee":"S. J. Henheik and S. Teufel, “Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap,” <i>Journal of Mathematical Physics</i>, vol. 63, no. 1. AIP Publishing, 2022.","short":"S.J. Henheik, S. Teufel, Journal of Mathematical Physics 63 (2022).","mla":"Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic Limit: Systems with a Uniform Gap.” <i>Journal of Mathematical Physics</i>, vol. 63, no. 1, 011901, AIP Publishing, 2022, doi:<a href=\"https://doi.org/10.1063/5.0051632\">10.1063/5.0051632</a>.","chicago":"Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic Limit: Systems with a Uniform Gap.” <i>Journal of Mathematical Physics</i>. AIP Publishing, 2022. <a href=\"https://doi.org/10.1063/5.0051632\">https://doi.org/10.1063/5.0051632</a>.","ama":"Henheik SJ, Teufel S. Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap. <i>Journal of Mathematical Physics</i>. 2022;63(1). doi:<a href=\"https://doi.org/10.1063/5.0051632\">10.1063/5.0051632</a>"},"project":[{"call_identifier":"H2020","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"intvolume":"        63","arxiv":1,"article_number":"011901","article_type":"original","acknowledgement":"J.H. acknowledges partial financial support from ERC Advanced Grant “RMTBeyond” No. 101020331.","external_id":{"isi":["000739446000009"],"arxiv":["2012.15238"]},"oa":1,"article_processing_charge":"No","date_created":"2022-01-03T12:19:48Z","year":"2022"},{"acknowledgement":"J.H. acknowledges partial financial support by the ERC Advanced Grant ‘RMTBeyond’ No. 101020331. Support for publication costs from the Deutsche Forschungsgemeinschaft and the Open Access Publishing Fund of the University of Tübingen is gratefully acknowledged.","external_id":{"isi":["000743615000001"],"arxiv":["2012.15239"]},"oa":1,"article_type":"original","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"article_processing_charge":"Yes","date_created":"2022-01-18T16:18:51Z","year":"2022","title":"Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk","date_updated":"2025-04-14T07:57:17Z","author":[{"orcid":"0000-0003-1106-327X","full_name":"Henheik, Sven Joscha","last_name":"Henheik","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha"},{"full_name":"Teufel, Stefan","last_name":"Teufel","first_name":"Stefan"}],"abstract":[{"lang":"eng","text":"We prove a generalised super-adiabatic theorem for extended fermionic systems assuming a spectral gap only in the bulk. More precisely, we assume that the infinite system has a unique ground state and that the corresponding Gelfand–Naimark–Segal Hamiltonian has a spectral gap above its eigenvalue zero. Moreover, we show that a similar adiabatic theorem also holds in the bulk of finite systems up to errors that vanish faster than any inverse power of the system size, although the corresponding finite-volume Hamiltonians need not have a spectral gap.\r\n\r\n"}],"arxiv":1,"article_number":"e4","day":"18","volume":10,"intvolume":"        10","citation":{"ista":"Henheik SJ, Teufel S. 2022. Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk. Forum of Mathematics, Sigma. 10, e4.","ieee":"S. J. Henheik and S. Teufel, “Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk,” <i>Forum of Mathematics, Sigma</i>, vol. 10. Cambridge University Press, 2022.","apa":"Henheik, S. J., &#38; Teufel, S. (2022). Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fms.2021.80\">https://doi.org/10.1017/fms.2021.80</a>","short":"S.J. Henheik, S. Teufel, Forum of Mathematics, Sigma 10 (2022).","mla":"Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic Limit: Systems with a Gap in the Bulk.” <i>Forum of Mathematics, Sigma</i>, vol. 10, e4, Cambridge University Press, 2022, doi:<a href=\"https://doi.org/10.1017/fms.2021.80\">10.1017/fms.2021.80</a>.","chicago":"Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic Limit: Systems with a Gap in the Bulk.” <i>Forum of Mathematics, Sigma</i>. Cambridge University Press, 2022. <a href=\"https://doi.org/10.1017/fms.2021.80\">https://doi.org/10.1017/fms.2021.80</a>.","ama":"Henheik SJ, Teufel S. Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk. <i>Forum of Mathematics, Sigma</i>. 2022;10. doi:<a href=\"https://doi.org/10.1017/fms.2021.80\">10.1017/fms.2021.80</a>"},"project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","call_identifier":"H2020"}],"date_published":"2022-01-18T00:00:00Z","has_accepted_license":"1","file_date_updated":"2022-01-19T09:27:43Z","status":"public","keyword":["computational mathematics","discrete mathematics and combinatorics","geometry and topology","mathematical physics","statistics and probability","algebra and number theory","theoretical computer science","analysis"],"quality_controlled":"1","corr_author":"1","license":"https://creativecommons.org/licenses/by/4.0/","doi":"10.1017/fms.2021.80","publication_identifier":{"eissn":["2050-5094"]},"file":[{"file_name":"2022_ForumMathSigma_Henheik.pdf","file_size":705323,"checksum":"87592a755adcef22ea590a99dc728dd3","file_id":"10646","date_updated":"2022-01-19T09:27:43Z","creator":"cchlebak","access_level":"open_access","content_type":"application/pdf","date_created":"2022-01-19T09:27:43Z","relation":"main_file","success":1}],"fulldoi":"https://doi.org/10.1017/fms.2021.80","ec_funded":1,"department":[{"_id":"GradSch"},{"_id":"LaEr"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication_status":"published","publication":"Forum of Mathematics, Sigma","language":[{"iso":"eng"}],"type":"journal_article","publisher":"Cambridge University Press","ddc":["510"],"month":"01","scopus_import":"1","_id":"10643","oa_version":"Published Version","isi":1},{"day":"15","volume":282,"intvolume":"       282","citation":{"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.","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>","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Journal of Functional Analysis 282 (2022).","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>.","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>."},"arxiv":1,"article_number":"109394","author":[{"first_name":"Giorgio","last_name":"Cipolloni","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio"},{"orcid":"0000-0001-5366-9603","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","first_name":"László"},{"first_name":"Dominik J","last_name":"Schröder","id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J"}],"abstract":[{"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.","lang":"eng"}],"title":"Thermalisation for Wigner matrices","date_updated":"2024-10-09T21:01:33Z","article_processing_charge":"Yes (via OA deal)","date_created":"2022-02-06T23:01:30Z","year":"2022","article_type":"original","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"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.","external_id":{"isi":["000781239100004"],"arxiv":["2102.09975"]},"oa":1,"ddc":["500"],"month":"04","_id":"10732","oa_version":"Published Version","scopus_import":"1","isi":1,"type":"journal_article","publisher":"Elsevier","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication_status":"published","publication":"Journal of Functional Analysis","language":[{"iso":"eng"}],"fulldoi":"https://doi.org/10.1016/j.jfa.2022.109394","department":[{"_id":"LaEr"}],"quality_controlled":"1","corr_author":"1","publication_identifier":{"issn":["0022-1236"],"eissn":["1096-0783"]},"doi":"10.1016/j.jfa.2022.109394","file":[{"file_id":"11690","creator":"dernst","date_updated":"2022-07-29T07:22:08Z","access_level":"open_access","file_name":"2022_JourFunctionalAnalysis_Cipolloni.pdf","file_size":652573,"checksum":"b75fdad606ab507dc61109e0907d86c0","relation":"main_file","success":1,"content_type":"application/pdf","date_created":"2022-07-29T07:22:08Z"}],"issue":"8","file_date_updated":"2022-07-29T07:22:08Z","status":"public","date_published":"2022-04-15T00:00:00Z","has_accepted_license":"1"},{"related_material":{"record":[{"relation":"dissertation_contains","id":"19540","status":"public"}]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_status":"published","language":[{"iso":"eng"}],"publication":"Letters in Mathematical Physics","type":"journal_article","publisher":"Springer Nature","_id":"10642","scopus_import":"1","oa_version":"Published Version","isi":1,"ddc":["530"],"month":"01","date_published":"2022-01-18T00:00:00Z","has_accepted_license":"1","keyword":["mathematical physics","statistical and nonlinear physics"],"file_date_updated":"2022-01-19T09:41:14Z","issue":"1","status":"public","pmid":1,"file":[{"relation":"main_file","success":1,"content_type":"application/pdf","date_created":"2022-01-19T09:41:14Z","file_id":"10647","access_level":"open_access","creator":"cchlebak","date_updated":"2022-01-19T09:41:14Z","file_name":"2022_LettersMathPhys_Henheik.pdf","checksum":"7e8e69b76e892c305071a4736131fe18","file_size":357547}],"publication_identifier":{"eissn":["1573-0530"],"issn":["0377-9017"]},"doi":"10.1007/s11005-021-01494-y","quality_controlled":"1","ec_funded":1,"department":[{"_id":"GradSch"},{"_id":"LaEr"}],"fulldoi":"https://doi.org/10.1007/s11005-021-01494-y","date_updated":"2026-07-29T13:18:16Z","title":"Local stability of ground states in locally gapped and weakly interacting quantum spin systems","author":[{"full_name":"Henheik, Sven Joscha","orcid":"0000-0003-1106-327X","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","last_name":"Henheik","first_name":"Sven Joscha"},{"last_name":"Teufel","first_name":"Stefan","full_name":"Teufel, Stefan"},{"full_name":"Wessel, Tom","first_name":"Tom","last_name":"Wessel"}],"abstract":[{"lang":"eng","text":"Based on a result by Yarotsky (J Stat Phys 118, 2005), we prove that localized but otherwise arbitrary perturbations of weakly interacting quantum spin systems with uniformly gapped on-site terms change the ground state of such a system only locally, even if they close the spectral gap. We call this a strong version of the local perturbations perturb locally (LPPL) principle which is known to hold for much more general gapped systems, but only for perturbations that do not close the spectral gap of the Hamiltonian. We also extend this strong LPPL-principle to Hamiltonians that have the appropriate structure of gapped on-site terms and weak interactions only locally in some region of space. While our results are technically corollaries to a theorem of Yarotsky, we expect that the paradigm of systems with a locally gapped ground state that is completely insensitive to the form of the Hamiltonian elsewhere extends to other situations and has important physical consequences."}],"article_number":"9","arxiv":1,"volume":112,"project":[{"call_identifier":"H2020","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"intvolume":"       112","citation":{"ama":"Henheik SJ, Teufel S, Wessel T. Local stability of ground states in locally gapped and weakly interacting quantum spin systems. <i>Letters in Mathematical Physics</i>. 2022;112(1). doi:<a href=\"https://doi.org/10.1007/s11005-021-01494-y\">10.1007/s11005-021-01494-y</a>","short":"S.J. Henheik, S. Teufel, T. Wessel, Letters in Mathematical Physics 112 (2022).","mla":"Henheik, Sven Joscha, et al. “Local Stability of Ground States in Locally Gapped and Weakly Interacting Quantum Spin Systems.” <i>Letters in Mathematical Physics</i>, vol. 112, no. 1, 9, Springer Nature, 2022, doi:<a href=\"https://doi.org/10.1007/s11005-021-01494-y\">10.1007/s11005-021-01494-y</a>.","chicago":"Henheik, Sven Joscha, Stefan Teufel, and Tom Wessel. “Local Stability of Ground States in Locally Gapped and Weakly Interacting Quantum Spin Systems.” <i>Letters in Mathematical Physics</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s11005-021-01494-y\">https://doi.org/10.1007/s11005-021-01494-y</a>.","ista":"Henheik SJ, Teufel S, Wessel T. 2022. Local stability of ground states in locally gapped and weakly interacting quantum spin systems. Letters in Mathematical Physics. 112(1), 9.","ieee":"S. J. Henheik, S. Teufel, and T. Wessel, “Local stability of ground states in locally gapped and weakly interacting quantum spin systems,” <i>Letters in Mathematical Physics</i>, vol. 112, no. 1. Springer Nature, 2022.","apa":"Henheik, S. J., Teufel, S., &#38; Wessel, T. (2022). Local stability of ground states in locally gapped and weakly interacting quantum spin systems. <i>Letters in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s11005-021-01494-y\">https://doi.org/10.1007/s11005-021-01494-y</a>"},"day":"18","external_id":{"isi":["000744930400001"],"arxiv":["2106.13780"],"pmid":["35125630"]},"oa":1,"acknowledgement":"J. H. acknowledges partial financial support by the ERC Advanced Grant “RMTBeyond” No. 101020331. S. T. thanks Marius Lemm and Simone Warzel for very helpful comments and discussions and Jürg Fröhlich for references to the literature. Open Access funding enabled and organized by Projekt DEAL.","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"article_type":"original","date_created":"2022-01-18T16:18:25Z","year":"2022","article_processing_charge":"No"},{"date_published":"2022-01-11T00:00:00Z","has_accepted_license":"1","file_date_updated":"2022-01-14T07:27:45Z","status":"public","keyword":["geometry and topology","mathematical physics"],"issue":"1","doi":"10.1007/s11040-021-09415-0","publication_identifier":{"eissn":["1572-9656"],"issn":["1385-0172"]},"file":[{"access_level":"open_access","date_updated":"2022-01-14T07:27:45Z","creator":"cchlebak","file_id":"10624","checksum":"d44f8123a52592a75b2c3b8ee2cd2435","file_size":505804,"file_name":"2022_MathPhyAnalGeo_Henheik.pdf","success":1,"relation":"main_file","date_created":"2022-01-14T07:27:45Z","content_type":"application/pdf"}],"quality_controlled":"1","corr_author":"1","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"ec_funded":1,"fulldoi":"https://doi.org/10.1007/s11040-021-09415-0","related_material":{"record":[{"relation":"dissertation_contains","id":"19540","status":"public"}]},"publication_status":"published","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication":"Mathematical Physics, Analysis and Geometry","language":[{"iso":"eng"}],"type":"journal_article","publisher":"Springer Nature","_id":"10623","oa_version":"Published Version","scopus_import":"1","isi":1,"ddc":["514"],"month":"01","external_id":{"arxiv":["2106.02015"],"isi":["000741387600001"]},"oa":1,"acknowledgement":"I am very grateful to Robert Seiringer for his guidance during this project and for many valuable comments on an earlier version of the manuscript. Moreover, I would like to thank Asbjørn Bækgaard Lauritsen for many helpful discussions and comments, pointing out the reference [22] and for his involvement in a closely related joint project [13]. Finally, I am grateful to Christian Hainzl for valuable comments on an earlier version of the manuscript and Andreas Deuchert for interesting discussions.","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"article_type":"original","year":"2022","date_created":"2022-01-13T15:40:53Z","article_processing_charge":"Yes (via OA deal)","date_updated":"2026-07-29T13:18:16Z","title":"The BCS critical temperature at high density","abstract":[{"lang":"eng","text":"We investigate the BCS critical temperature Tc in the high-density limit and derive an asymptotic formula, which strongly depends on the behavior of the interaction potential V on the Fermi-surface. Our results include a rigorous confirmation for the behavior of Tc at high densities proposed by Langmann et al. (Phys Rev Lett 122:157001, 2019) and identify precise conditions under which superconducting domes arise in BCS theory."}],"author":[{"id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","last_name":"Henheik","first_name":"Sven Joscha","full_name":"Henheik, Sven Joscha","orcid":"0000-0003-1106-327X"}],"article_number":"3","arxiv":1,"volume":25,"project":[{"call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"intvolume":"        25","citation":{"apa":"Henheik, S. J. (2022). The BCS critical temperature at high density. <i>Mathematical Physics, Analysis and Geometry</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s11040-021-09415-0\">https://doi.org/10.1007/s11040-021-09415-0</a>","ieee":"S. J. Henheik, “The BCS critical temperature at high density,” <i>Mathematical Physics, Analysis and Geometry</i>, vol. 25, no. 1. Springer Nature, 2022.","ista":"Henheik SJ. 2022. The BCS critical temperature at high density. Mathematical Physics, Analysis and Geometry. 25(1), 3.","chicago":"Henheik, Sven Joscha. “The BCS Critical Temperature at High Density.” <i>Mathematical Physics, Analysis and Geometry</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s11040-021-09415-0\">https://doi.org/10.1007/s11040-021-09415-0</a>.","mla":"Henheik, Sven Joscha. “The BCS Critical Temperature at High Density.” <i>Mathematical Physics, Analysis and Geometry</i>, vol. 25, no. 1, 3, Springer Nature, 2022, doi:<a href=\"https://doi.org/10.1007/s11040-021-09415-0\">10.1007/s11040-021-09415-0</a>.","short":"S.J. Henheik, Mathematical Physics, Analysis and Geometry 25 (2022).","ama":"Henheik SJ. The BCS critical temperature at high density. <i>Mathematical Physics, Analysis and Geometry</i>. 2022;25(1). doi:<a href=\"https://doi.org/10.1007/s11040-021-09415-0\">10.1007/s11040-021-09415-0</a>"},"day":"11"},{"corr_author":"1","quality_controlled":"1","publication_identifier":{"issn":["0022-2488"]},"file":[{"success":1,"relation":"main_file","date_created":"2023-01-27T07:10:52Z","content_type":"application/pdf","access_level":"open_access","date_updated":"2023-01-27T07:10:52Z","creator":"dernst","file_id":"12410","checksum":"213b93750080460718c050e4967cfdb4","file_size":5251092,"file_name":"2022_JourMathPhysics_Henheik2.pdf"}],"doi":"10.1063/5.0123441","fulldoi":"https://doi.org/10.1063/5.0123441","ec_funded":1,"department":[{"_id":"LaEr"}],"has_accepted_license":"1","date_published":"2022-12-01T00:00:00Z","status":"public","file_date_updated":"2023-01-27T07:10:52Z","issue":"12","ddc":["510"],"month":"12","isi":1,"oa_version":"Published Version","_id":"12184","scopus_import":"1","publication":"Journal of Mathematical Physics","language":[{"iso":"eng"}],"publication_status":"published","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"19540"}]},"publisher":"AIP Publishing","type":"journal_article","article_processing_charge":"No","year":"2022","date_created":"2023-01-15T23:00:52Z","acknowledgement":"It is a pleasure to thank Stefan Teufel for numerous interesting discussions, fruitful collaboration, and many helpful comments on an earlier version of the manuscript. J.H. acknowledges partial financial support from the ERC Advanced Grant No. 101020331 “Random\r\nmatrices beyond Wigner-Dyson-Mehta.” T.W. acknowledges financial support from the DFG research unit FOR 5413 “Long-range interacting quantum spin systems out of equilibrium: Experiment, Theory and Mathematics.\" ","oa":1,"external_id":{"isi":["000905776200001"],"arxiv":["2208.12220"]},"article_type":"original","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"arxiv":1,"article_number":"121101","day":"01","citation":{"ama":"Henheik SJ, Wessel T. On adiabatic theory for extended fermionic lattice systems. <i>Journal of Mathematical Physics</i>. 2022;63(12). doi:<a href=\"https://doi.org/10.1063/5.0123441\">10.1063/5.0123441</a>","chicago":"Henheik, Sven Joscha, and Tom Wessel. “On Adiabatic Theory for Extended Fermionic Lattice Systems.” <i>Journal of Mathematical Physics</i>. AIP Publishing, 2022. <a href=\"https://doi.org/10.1063/5.0123441\">https://doi.org/10.1063/5.0123441</a>.","short":"S.J. Henheik, T. Wessel, Journal of Mathematical Physics 63 (2022).","mla":"Henheik, Sven Joscha, and Tom Wessel. “On Adiabatic Theory for Extended Fermionic Lattice Systems.” <i>Journal of Mathematical Physics</i>, vol. 63, no. 12, 121101, AIP Publishing, 2022, doi:<a href=\"https://doi.org/10.1063/5.0123441\">10.1063/5.0123441</a>.","ieee":"S. J. Henheik and T. Wessel, “On adiabatic theory for extended fermionic lattice systems,” <i>Journal of Mathematical Physics</i>, vol. 63, no. 12. AIP Publishing, 2022.","apa":"Henheik, S. J., &#38; Wessel, T. (2022). On adiabatic theory for extended fermionic lattice systems. <i>Journal of Mathematical Physics</i>. AIP Publishing. <a href=\"https://doi.org/10.1063/5.0123441\">https://doi.org/10.1063/5.0123441</a>","ista":"Henheik SJ, Wessel T. 2022. On adiabatic theory for extended fermionic lattice systems. Journal of Mathematical Physics. 63(12), 121101."},"intvolume":"        63","project":[{"call_identifier":"H2020","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"volume":63,"title":"On adiabatic theory for extended fermionic lattice systems","date_updated":"2026-07-29T13:18:16Z","author":[{"first_name":"Sven Joscha","last_name":"Henheik","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","orcid":"0000-0003-1106-327X","full_name":"Henheik, Sven Joscha"},{"full_name":"Wessel, Tom","last_name":"Wessel","first_name":"Tom"}],"abstract":[{"text":"We review recent results on adiabatic theory for ground states of extended gapped fermionic lattice systems under several different assumptions. More precisely, we present generalized super-adiabatic theorems for extended but finite and infinite systems, assuming either a uniform gap or a gap in the bulk above the unperturbed ground state. The goal of this Review is to provide an overview of these adiabatic theorems and briefly outline the main ideas and techniques required in their proofs.","lang":"eng"}]},{"title":"On the operator norm of a Hermitian random matrix with correlated entries","date_updated":"2026-10-02T11:31:29Z","author":[{"full_name":"Reker, Jana","id":"e796e4f9-dc8d-11ea-abe3-97e26a0323e9","last_name":"Reker","first_name":"Jana"}],"abstract":[{"text":"We consider a correlated NxN Hermitian random matrix with a polynomially decaying metric correlation structure. By calculating the trace of the moments of the matrix and using the summable decay of the cumulants, we show that its operator norm is stochastically dominated by one.","lang":"eng"}],"arxiv":1,"article_number":"2250036","day":"01","intvolume":"        11","citation":{"ama":"Reker J. On the operator norm of a Hermitian random matrix with correlated entries. <i>Random Matrices: Theory and Applications</i>. 2022;11(4). doi:<a href=\"https://doi.org/10.1142/s2010326322500368\">10.1142/s2010326322500368</a>","mla":"Reker, Jana. “On the Operator Norm of a Hermitian Random Matrix with Correlated Entries.” <i>Random Matrices: Theory and Applications</i>, vol. 11, no. 4, 2250036, World Scientific Publishing, 2022, doi:<a href=\"https://doi.org/10.1142/s2010326322500368\">10.1142/s2010326322500368</a>.","short":"J. Reker, Random Matrices: Theory and Applications 11 (2022).","chicago":"Reker, Jana. “On the Operator Norm of a Hermitian Random Matrix with Correlated Entries.” <i>Random Matrices: Theory and Applications</i>. World Scientific Publishing, 2022. <a href=\"https://doi.org/10.1142/s2010326322500368\">https://doi.org/10.1142/s2010326322500368</a>.","ista":"Reker J. 2022. On the operator norm of a Hermitian random matrix with correlated entries. Random Matrices: Theory and Applications. 11(4), 2250036.","ieee":"J. Reker, “On the operator norm of a Hermitian random matrix with correlated entries,” <i>Random Matrices: Theory and Applications</i>, vol. 11, no. 4. World Scientific Publishing, 2022.","apa":"Reker, J. (2022). On the operator norm of a Hermitian random matrix with correlated entries. <i>Random Matrices: Theory and Applications</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/s2010326322500368\">https://doi.org/10.1142/s2010326322500368</a>"},"volume":11,"oa":1,"external_id":{"isi":["000848873800001"],"arxiv":["2103.03906"]},"article_type":"original","article_processing_charge":"No","year":"2022","date_created":"2022-04-08T07:11:12Z","language":[{"iso":"eng"}],"publication":"Random Matrices: Theory and Applications","publication_status":"published","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","related_material":{"record":[{"relation":"dissertation_contains","id":"17164","status":"public"}]},"main_file_link":[{"url":" https://doi.org/10.48550/arXiv.2103.03906","open_access":"1"}],"publisher":"World Scientific Publishing","type":"journal_article","month":"10","isi":1,"_id":"11135","oa_version":"Preprint","scopus_import":"1","date_published":"2022-10-01T00:00:00Z","keyword":["Discrete Mathematics and Combinatorics","Statistics","Probability and Uncertainty","Statistics and Probability","Algebra and Number Theory"],"issue":"4","status":"public","corr_author":"1","quality_controlled":"1","doi":"10.1142/s2010326322500368","publication_identifier":{"eissn":["2010-3271"],"issn":["2010-3263"]},"fulldoi":"https://doi.org/10.1142/s2010326322500368","department":[{"_id":"GradSch"},{"_id":"LaEr"}]},{"type":"journal_article","publisher":"Springer Nature","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","publication_status":"published","publication":"Journal of Statistical Physics","language":[{"iso":"eng"}],"related_material":{"record":[{"id":"19540","relation":"dissertation_contains","status":"public"},{"id":"18135","relation":"dissertation_contains","status":"public"}]},"ddc":["530"],"month":"07","oa_version":"Published Version","_id":"11732","scopus_import":"1","isi":1,"status":"public","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"file_date_updated":"2022-08-08T07:36:34Z","date_published":"2022-07-29T00:00:00Z","has_accepted_license":"1","fulldoi":"https://doi.org/10.1007/s10955-022-02965-9","ec_funded":1,"department":[{"_id":"GradSch"},{"_id":"LaEr"},{"_id":"RoSe"}],"quality_controlled":"1","corr_author":"1","file":[{"file_size":419563,"checksum":"b398c4dbf65f71d417981d6e366427e9","file_name":"2022_JourStatisticalPhysics_Henheik.pdf","access_level":"open_access","creator":"dernst","date_updated":"2022-08-08T07:36:34Z","file_id":"11746","date_created":"2022-08-08T07:36:34Z","content_type":"application/pdf","success":1,"relation":"main_file"}],"doi":"10.1007/s10955-022-02965-9","publication_identifier":{"eissn":["1572-9613"],"issn":["0022-4715"]},"abstract":[{"text":"We study the BCS energy gap Ξ in the high–density limit and derive an asymptotic formula, which strongly depends on the strength of the interaction potential V on the Fermi surface. In combination with the recent result by one of us (Math. Phys. Anal. Geom. 25, 3, 2022) on the critical temperature Tc at high densities, we prove the universality of the ratio of the energy gap and the critical temperature.","lang":"eng"}],"author":[{"first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","last_name":"Henheik","orcid":"0000-0003-1106-327X","full_name":"Henheik, Sven Joscha"},{"last_name":"Lauritsen","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1","first_name":"Asbjørn Bækgaard","full_name":"Lauritsen, Asbjørn Bækgaard","orcid":"0000-0003-4476-2288"}],"title":"The BCS energy gap at high density","date_updated":"2026-10-02T11:43:00Z","day":"29","volume":189,"project":[{"grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020"}],"intvolume":"       189","citation":{"ama":"Henheik SJ, Lauritsen AB. The BCS energy gap at high density. <i>Journal of Statistical Physics</i>. 2022;189. doi:<a href=\"https://doi.org/10.1007/s10955-022-02965-9\">10.1007/s10955-022-02965-9</a>","chicago":"Henheik, Sven Joscha, and Asbjørn Bækgaard Lauritsen. “The BCS Energy Gap at High Density.” <i>Journal of Statistical Physics</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s10955-022-02965-9\">https://doi.org/10.1007/s10955-022-02965-9</a>.","short":"S.J. Henheik, A.B. Lauritsen, Journal of Statistical Physics 189 (2022).","mla":"Henheik, Sven Joscha, and Asbjørn Bækgaard Lauritsen. “The BCS Energy Gap at High Density.” <i>Journal of Statistical Physics</i>, vol. 189, 5, Springer Nature, 2022, doi:<a href=\"https://doi.org/10.1007/s10955-022-02965-9\">10.1007/s10955-022-02965-9</a>.","apa":"Henheik, S. J., &#38; Lauritsen, A. B. (2022). The BCS energy gap at high density. <i>Journal of Statistical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s10955-022-02965-9\">https://doi.org/10.1007/s10955-022-02965-9</a>","ieee":"S. J. Henheik and A. B. Lauritsen, “The BCS energy gap at high density,” <i>Journal of Statistical Physics</i>, vol. 189. Springer Nature, 2022.","ista":"Henheik SJ, Lauritsen AB. 2022. The BCS energy gap at high density. Journal of Statistical Physics. 189, 5."},"article_number":"5","article_type":"original","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"acknowledgement":"We are grateful to Robert Seiringer for helpful discussions and many valuable comments\r\non an earlier version of the manuscript. J.H. acknowledges partial financial support by the ERC Advanced Grant “RMTBeyond’ No. 101020331. Open access funding provided by Institute of Science and Technology (IST Austria)","external_id":{"isi":["000833007200002"]},"oa":1,"article_processing_charge":"Yes (via OA deal)","date_created":"2022-08-05T11:36:56Z","year":"2022"},{"oa":1,"external_id":{"arxiv":["1907.13631"]},"acknowledgement":"Partially supported by ERC Starting Grant RandMat No. 715539 and the SwissMap grant of Swiss National Science Foundation. Partially supported by ERC Advanced Grant RanMat No. 338804. Partially supported by the Hausdorff Center for Mathematics in Bonn.","article_type":"original","year":"2021","date_created":"2024-02-18T23:01:03Z","article_processing_charge":"No","date_updated":"2025-04-15T08:05:02Z","title":"Spectral radius of random matrices with independent entries","author":[{"full_name":"Alt, Johannes","first_name":"Johannes","last_name":"Alt","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","first_name":"László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Torben H","last_name":"Krüger","id":"3020C786-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4821-3297","full_name":"Krüger, Torben H"}],"abstract":[{"text":"We consider random n×n matrices X with independent and centered entries and a general variance profile. We show that the spectral radius of X converges with very high probability to the square root of the spectral radius of the variance matrix of X when n tends to infinity. We also establish the optimal rate of convergence, that is a new result even for general i.i.d. matrices beyond the explicitly solvable Gaussian cases. The main ingredient is the proof of the local inhomogeneous circular law [arXiv:1612.07776] at the spectral edge.","lang":"eng"}],"arxiv":1,"intvolume":"         2","project":[{"call_identifier":"FP7","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"citation":{"chicago":"Alt, Johannes, László Erdös, and Torben H Krüger. “Spectral Radius of Random Matrices with Independent Entries.” <i>Probability and Mathematical Physics</i>. Mathematical Sciences Publishers, 2021. <a href=\"https://doi.org/10.2140/pmp.2021.2.221\">https://doi.org/10.2140/pmp.2021.2.221</a>.","short":"J. Alt, L. Erdös, T.H. Krüger, Probability and Mathematical Physics 2 (2021) 221–280.","mla":"Alt, Johannes, et al. “Spectral Radius of Random Matrices with Independent Entries.” <i>Probability and Mathematical Physics</i>, vol. 2, no. 2, Mathematical Sciences Publishers, 2021, pp. 221–80, doi:<a href=\"https://doi.org/10.2140/pmp.2021.2.221\">10.2140/pmp.2021.2.221</a>.","ieee":"J. Alt, L. Erdös, and T. H. Krüger, “Spectral radius of random matrices with independent entries,” <i>Probability and Mathematical Physics</i>, vol. 2, no. 2. Mathematical Sciences Publishers, pp. 221–280, 2021.","apa":"Alt, J., Erdös, L., &#38; Krüger, T. H. (2021). Spectral radius of random matrices with independent entries. <i>Probability and Mathematical Physics</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/pmp.2021.2.221\">https://doi.org/10.2140/pmp.2021.2.221</a>","ista":"Alt J, Erdös L, Krüger TH. 2021. Spectral radius of random matrices with independent entries. Probability and Mathematical Physics. 2(2), 221–280.","ama":"Alt J, Erdös L, Krüger TH. Spectral radius of random matrices with independent entries. <i>Probability and Mathematical Physics</i>. 2021;2(2):221-280. doi:<a href=\"https://doi.org/10.2140/pmp.2021.2.221\">10.2140/pmp.2021.2.221</a>"},"volume":2,"day":"21","date_published":"2021-05-21T00:00:00Z","status":"public","issue":"2","doi":"10.2140/pmp.2021.2.221","publication_identifier":{"issn":["2690-0998"],"eissn":["2690-1005"]},"corr_author":"1","quality_controlled":"1","ec_funded":1,"department":[{"_id":"LaEr"}],"fulldoi":"https://doi.org/10.2140/pmp.2021.2.221","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1907.13631","open_access":"1"}],"language":[{"iso":"eng"}],"publication":"Probability and Mathematical Physics","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_status":"published","publisher":"Mathematical Sciences Publishers","type":"journal_article","oa_version":"Preprint","_id":"15013","scopus_import":"1","month":"05","page":"221-280"},{"type":"journal_article","publisher":"Institute of Mathematical Statistics","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1904.04312"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","publication_status":"published","publication":"The Annals of Probability","language":[{"iso":"eng"}],"page":"1886-1916","_id":"15259","oa_version":"Preprint","scopus_import":"1","isi":1,"month":"07","issue":"4","keyword":["Statistics","Probability and Uncertainty","Statistics and Probability"],"status":"public","date_published":"2021-07-01T00:00:00Z","ec_funded":1,"department":[{"_id":"LaEr"}],"fulldoi":"https://doi.org/10.1214/20-aop1496","publication_identifier":{"issn":["0091-1798"]},"doi":"10.1214/20-aop1496","quality_controlled":"1","corr_author":"1","abstract":[{"text":"We consider words Gi1⋯Gim involving i.i.d. complex Ginibre matrices and study tracial expressions of their eigenvalues and singular values. We show that the limit distribution of the squared singular values of every word of length m is a Fuss–Catalan distribution with parameter \r\nm+1. This generalizes previous results concerning powers of a complex Ginibre matrix and products of independent Ginibre matrices. In addition, we find other combinatorial parameters of the word that determine the second-order limits of the spectral statistics. For instance, the so-called coperiod of a word characterizes the fluctuations of the eigenvalues. We extend these results to words of general non-Hermitian matrices with i.i.d. entries under moment-matching assumptions, band matrices, and sparse matrices.\r\nThese results rely on the moments method and genus expansion, relating Gaussian matrix integrals to the counting of compact orientable surfaces of a given genus. This allows us to derive a central limit theorem for the trace of any word of complex Ginibre matrices and their conjugate transposes, where all parameters are defined topologically.","lang":"eng"}],"author":[{"full_name":"Dubach, Guillaume","orcid":"0000-0001-6892-8137","last_name":"Dubach","id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E","first_name":"Guillaume"},{"last_name":"Peled","first_name":"Yuval","full_name":"Peled, Yuval"}],"date_updated":"2025-09-10T10:13:20Z","title":"On words of non-Hermitian random matrices","volume":49,"project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","call_identifier":"H2020"}],"intvolume":"        49","citation":{"ama":"Dubach G, Peled Y. On words of non-Hermitian random matrices. <i>The Annals of Probability</i>. 2021;49(4):1886-1916. doi:<a href=\"https://doi.org/10.1214/20-aop1496\">10.1214/20-aop1496</a>","ista":"Dubach G, Peled Y. 2021. On words of non-Hermitian random matrices. The Annals of Probability. 49(4), 1886–1916.","ieee":"G. Dubach and Y. Peled, “On words of non-Hermitian random matrices,” <i>The Annals of Probability</i>, vol. 49, no. 4. Institute of Mathematical Statistics, pp. 1886–1916, 2021.","apa":"Dubach, G., &#38; Peled, Y. (2021). On words of non-Hermitian random matrices. <i>The Annals of Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/20-aop1496\">https://doi.org/10.1214/20-aop1496</a>","short":"G. Dubach, Y. Peled, The Annals of Probability 49 (2021) 1886–1916.","mla":"Dubach, Guillaume, and Yuval Peled. “On Words of Non-Hermitian Random Matrices.” <i>The Annals of Probability</i>, vol. 49, no. 4, Institute of Mathematical Statistics, 2021, pp. 1886–916, doi:<a href=\"https://doi.org/10.1214/20-aop1496\">10.1214/20-aop1496</a>.","chicago":"Dubach, Guillaume, and Yuval Peled. “On Words of Non-Hermitian Random Matrices.” <i>The Annals of Probability</i>. Institute of Mathematical Statistics, 2021. <a href=\"https://doi.org/10.1214/20-aop1496\">https://doi.org/10.1214/20-aop1496</a>."},"day":"01","arxiv":1,"article_type":"original","external_id":{"isi":["000681349000008"],"arxiv":["1904.04312"]},"oa":1,"acknowledgement":"The authors would like to thank Gernot Akemann, Benson Au, Paul Bourgade, Jesper Ipsen, Camille Male, Jamie Mingo, Doron Puder, Emily Redelmeier, Roland Speicher, Wojciech Tarnowski and Ofer Zeitouni for useful discussions, comments and references as well as the anonymous referee for a suggestion that greatly improved one of the theorems.\r\nG.D. gratefully acknowledges support from the grants NSF DMS-1812114 of P. Bourgade (PI) and NSF CAREER DMS-1653602 of L.-P. Arguin (PI), as well as the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411.","year":"2021","date_created":"2024-04-03T07:19:42Z","article_processing_charge":"No"},{"article_processing_charge":"Yes (via OA deal)","year":"2021","date_created":"2021-11-07T23:01:25Z","article_type":"original","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria).","external_id":{"arxiv":["2012.13215"],"isi":["000712232700001"]},"oa":1,"day":"29","volume":388,"project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"intvolume":"       388","citation":{"ama":"Cipolloni G, Erdös L, Schröder DJ. Eigenstate thermalization hypothesis for Wigner matrices. <i>Communications in Mathematical Physics</i>. 2021;388(2):1005–1048. doi:<a href=\"https://doi.org/10.1007/s00220-021-04239-z\">10.1007/s00220-021-04239-z</a>","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Communications in Mathematical Physics 388 (2021) 1005–1048.","mla":"Cipolloni, Giorgio, et al. “Eigenstate Thermalization Hypothesis for Wigner Matrices.” <i>Communications in Mathematical Physics</i>, vol. 388, no. 2, Springer Nature, 2021, pp. 1005–1048, doi:<a href=\"https://doi.org/10.1007/s00220-021-04239-z\">10.1007/s00220-021-04239-z</a>.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Eigenstate Thermalization Hypothesis for Wigner Matrices.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00220-021-04239-z\">https://doi.org/10.1007/s00220-021-04239-z</a>.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2021. Eigenstate thermalization hypothesis for Wigner matrices. Communications in Mathematical Physics. 388(2), 1005–1048.","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2021). Eigenstate thermalization hypothesis for Wigner matrices. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-021-04239-z\">https://doi.org/10.1007/s00220-021-04239-z</a>","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Eigenstate thermalization hypothesis for Wigner matrices,” <i>Communications in Mathematical Physics</i>, vol. 388, no. 2. Springer Nature, pp. 1005–1048, 2021."},"arxiv":1,"author":[{"orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio","last_name":"Cipolloni","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio"},{"first_name":"László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","full_name":"Erdös, László"},{"first_name":"Dominik J","last_name":"Schröder","id":"408ED176-F248-11E8-B48F-1D18A9856A87","full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856"}],"abstract":[{"text":"We prove that any deterministic matrix is approximately the identity in the eigenbasis of a large random Wigner matrix with very high probability and with an optimal error inversely proportional to the square root of the dimension. Our theorem thus rigorously verifies the Eigenstate Thermalisation Hypothesis by Deutsch (Phys Rev A 43:2046–2049, 1991) for the simplest chaotic quantum system, the Wigner ensemble. In mathematical terms, we prove the strong form of Quantum Unique Ergodicity (QUE) with an optimal convergence rate for all eigenvectors simultaneously, generalizing previous probabilistic QUE results in Bourgade and Yau (Commun Math Phys 350:231–278, 2017) and Bourgade et al. (Commun Pure Appl Math 73:1526–1596, 2020).","lang":"eng"}],"title":"Eigenstate thermalization hypothesis for Wigner matrices","date_updated":"2025-04-15T06:53:08Z","fulldoi":"https://doi.org/10.1007/s00220-021-04239-z","department":[{"_id":"LaEr"}],"quality_controlled":"1","corr_author":"1","publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"file":[{"checksum":"a2c7b6f5d23b5453cd70d1261272283b","file_size":841426,"file_name":"2021_CommunMathPhys_Cipolloni.pdf","access_level":"open_access","date_updated":"2022-02-02T10:19:55Z","creator":"cchlebak","file_id":"10715","date_created":"2022-02-02T10:19:55Z","content_type":"application/pdf","success":1,"relation":"main_file"}],"doi":"10.1007/s00220-021-04239-z","status":"public","issue":"2","file_date_updated":"2022-02-02T10:19:55Z","date_published":"2021-10-29T00:00:00Z","has_accepted_license":"1","page":"1005–1048","month":"10","ddc":["510"],"oa_version":"Published Version","_id":"10221","scopus_import":"1","isi":1,"type":"journal_article","publisher":"Springer Nature","publication_status":"published","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","language":[{"iso":"eng"}],"publication":"Communications in Mathematical Physics"},{"article_number":"124","volume":26,"citation":{"ama":"Dubach G. On eigenvector statistics in the spherical and truncated unitary ensembles. <i>Electronic Journal of Probability</i>. 2021;26. doi:<a href=\"https://doi.org/10.1214/21-EJP686\">10.1214/21-EJP686</a>","short":"G. Dubach, Electronic Journal of Probability 26 (2021).","mla":"Dubach, Guillaume. “On Eigenvector Statistics in the Spherical and Truncated Unitary Ensembles.” <i>Electronic Journal of Probability</i>, vol. 26, 124, Institute of Mathematical Statistics, 2021, doi:<a href=\"https://doi.org/10.1214/21-EJP686\">10.1214/21-EJP686</a>.","chicago":"Dubach, Guillaume. “On Eigenvector Statistics in the Spherical and Truncated Unitary Ensembles.” <i>Electronic Journal of Probability</i>. Institute of Mathematical Statistics, 2021. <a href=\"https://doi.org/10.1214/21-EJP686\">https://doi.org/10.1214/21-EJP686</a>.","ista":"Dubach G. 2021. On eigenvector statistics in the spherical and truncated unitary ensembles. Electronic Journal of Probability. 26, 124.","ieee":"G. Dubach, “On eigenvector statistics in the spherical and truncated unitary ensembles,” <i>Electronic Journal of Probability</i>, vol. 26. Institute of Mathematical Statistics, 2021.","apa":"Dubach, G. (2021). On eigenvector statistics in the spherical and truncated unitary ensembles. <i>Electronic Journal of Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/21-EJP686\">https://doi.org/10.1214/21-EJP686</a>"},"project":[{"call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411"}],"intvolume":"        26","day":"28","date_updated":"2025-04-14T07:43:47Z","title":"On eigenvector statistics in the spherical and truncated unitary ensembles","abstract":[{"lang":"eng","text":"We study the overlaps between right and left eigenvectors for random matrices of the spherical ensemble, as well as truncated unitary ensembles in the regime where half of the matrix at least is truncated. These two integrable models exhibit a form of duality, and the essential steps of our investigation can therefore be performed in parallel. In every case, conditionally on all eigenvalues, diagonal overlaps are shown to be distributed as a product of independent random variables with explicit distributions. This enables us to prove that the scaled diagonal overlaps, conditionally on one eigenvalue, converge in distribution to a heavy-tail limit, namely, the inverse of a γ2 distribution. We also provide formulae for the conditional expectation of diagonal and off-diagonal overlaps, either with respect to one eigenvalue, or with respect to the whole spectrum. These results, analogous to what is known for the complex Ginibre ensemble, can be obtained in these cases thanks to integration techniques inspired from a previous work by Forrester & Krishnapur."}],"author":[{"full_name":"Dubach, Guillaume","orcid":"0000-0001-6892-8137","first_name":"Guillaume","id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E","last_name":"Dubach"}],"year":"2021","date_created":"2021-11-14T23:01:25Z","article_processing_charge":"No","oa":1,"acknowledgement":"We acknowledge partial support from the grants NSF DMS-1812114 of P. Bourgade (PI) and NSF CAREER DMS-1653602 of L.-P. Arguin (PI). This project has also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411. We would like to thank Paul Bourgade and László Erdős for many helpful comments.","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"article_type":"original","_id":"10285","scopus_import":"1","oa_version":"Published Version","ddc":["519"],"month":"09","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","publication_status":"published","publication":"Electronic Journal of Probability","language":[{"iso":"eng"}],"type":"journal_article","publisher":"Institute of Mathematical Statistics","file":[{"file_name":"2021_ElecJournalProb_Dubach.pdf","checksum":"1c975afb31460277ce4d22b93538e5f9","file_size":735940,"file_id":"10288","access_level":"open_access","date_updated":"2021-11-15T10:10:17Z","creator":"cchlebak","content_type":"application/pdf","date_created":"2021-11-15T10:10:17Z","relation":"main_file","success":1}],"doi":"10.1214/21-EJP686","publication_identifier":{"eissn":["1083-6489"]},"quality_controlled":"1","department":[{"_id":"LaEr"}],"ec_funded":1,"fulldoi":"https://doi.org/10.1214/21-EJP686","date_published":"2021-09-28T00:00:00Z","has_accepted_license":"1","file_date_updated":"2021-11-15T10:10:17Z","status":"public"},{"publisher":"Elsevier","type":"journal_article","publication":"Linear Algebra and its Applications","language":[{"iso":"eng"}],"publication_status":"published","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2002.11678"}],"page":"203-217","month":"01","isi":1,"scopus_import":"1","_id":"8373","oa_version":"Preprint","keyword":["Kubo-Ando mean","weighted multivariate mean","barycenter"],"status":"public","date_published":"2021-01-15T00:00:00Z","fulldoi":"https://doi.org/10.1016/j.laa.2020.09.007","department":[{"_id":"LaEr"}],"ec_funded":1,"quality_controlled":"1","doi":"10.1016/j.laa.2020.09.007","publication_identifier":{"issn":["0024-3795"]},"author":[{"full_name":"Pitrik, József","last_name":"Pitrik","first_name":"József"},{"full_name":"Virosztek, Daniel","orcid":"0000-0003-1109-5511","first_name":"Daniel","last_name":"Virosztek","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87"}],"abstract":[{"text":"It is well known that special Kubo-Ando operator means admit divergence center interpretations, moreover, they are also mean squared error estimators for certain metrics on positive definite operators. In this paper we give a divergence center interpretation for every symmetric Kubo-Ando mean. This characterization of the symmetric means naturally leads to a definition of weighted and multivariate versions of a large class of symmetric Kubo-Ando means. We study elementary properties of these weighted multivariate means, and note in particular that in the special case of the geometric mean we recover the weighted A#H-mean introduced by Kim, Lawson, and Lim.","lang":"eng"}],"title":"A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means","date_updated":"2025-04-14T07:50:40Z","day":"15","citation":{"ama":"Pitrik J, Virosztek D. A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means. <i>Linear Algebra and its Applications</i>. 2021;609:203-217. doi:<a href=\"https://doi.org/10.1016/j.laa.2020.09.007\">10.1016/j.laa.2020.09.007</a>","ista":"Pitrik J, Virosztek D. 2021. A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means. Linear Algebra and its Applications. 609, 203–217.","ieee":"J. Pitrik and D. Virosztek, “A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means,” <i>Linear Algebra and its Applications</i>, vol. 609. Elsevier, pp. 203–217, 2021.","apa":"Pitrik, J., &#38; Virosztek, D. (2021). A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means. <i>Linear Algebra and Its Applications</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.laa.2020.09.007\">https://doi.org/10.1016/j.laa.2020.09.007</a>","short":"J. Pitrik, D. Virosztek, Linear Algebra and Its Applications 609 (2021) 203–217.","mla":"Pitrik, József, and Daniel Virosztek. “A Divergence Center Interpretation of General Symmetric Kubo-Ando Means, and Related Weighted Multivariate Operator Means.” <i>Linear Algebra and Its Applications</i>, vol. 609, Elsevier, 2021, pp. 203–17, doi:<a href=\"https://doi.org/10.1016/j.laa.2020.09.007\">10.1016/j.laa.2020.09.007</a>.","chicago":"Pitrik, József, and Daniel Virosztek. “A Divergence Center Interpretation of General Symmetric Kubo-Ando Means, and Related Weighted Multivariate Operator Means.” <i>Linear Algebra and Its Applications</i>. Elsevier, 2021. <a href=\"https://doi.org/10.1016/j.laa.2020.09.007\">https://doi.org/10.1016/j.laa.2020.09.007</a>."},"project":[{"name":"Geometric study of Wasserstein spaces and free probability","_id":"26A455A6-B435-11E9-9278-68D0E5697425","grant_number":"846294","call_identifier":"H2020"},{"call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425","name":"International IST Postdoc Fellowship Programme","grant_number":"291734"}],"intvolume":"       609","volume":609,"arxiv":1,"article_type":"original","acknowledgement":"The authors are grateful to Milán Mosonyi for fruitful discussions on the topic, and to the anonymous referee for his/her comments and suggestions.\r\nJ. Pitrik was supported by the Hungarian Academy of Sciences Lendület-Momentum Grant for Quantum Information Theory, No. 96 141, and by Hungarian National Research, Development and Innovation Office (NKFIH) via grants no. K119442, no. K124152, and no. KH129601. D. Virosztek was supported by the ISTFELLOW program of the Institute of Science and Technology Austria (project code IC1027FELL01), by the European Union's Horizon 2020 research and innovation program under the Marie Sklodowska-Curie Grant Agreement No. 846294, and partially supported by the Hungarian National Research, Development and Innovation Office (NKFIH) via grants no. K124152, and no. KH129601.","oa":1,"external_id":{"isi":["000581730500011"],"arxiv":["2002.11678"]},"article_processing_charge":"No","year":"2021","date_created":"2020-09-11T08:35:50Z"},{"arxiv":1,"day":"01","project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"},{"call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804"},{"name":"International IST Doctoral Program","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","grant_number":"665385","call_identifier":"H2020"}],"citation":{"ista":"Cipolloni G, Erdös L, Schröder DJ. 2021. Edge universality for non-Hermitian random matrices. Probability Theory and Related Fields.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Edge universality for non-Hermitian random matrices,” <i>Probability Theory and Related Fields</i>. Springer Nature, 2021.","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2021). Edge universality for non-Hermitian random matrices. <i>Probability Theory and Related Fields</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00440-020-01003-7\">https://doi.org/10.1007/s00440-020-01003-7</a>","mla":"Cipolloni, Giorgio, et al. “Edge Universality for Non-Hermitian Random Matrices.” <i>Probability Theory and Related Fields</i>, Springer Nature, 2021, doi:<a href=\"https://doi.org/10.1007/s00440-020-01003-7\">10.1007/s00440-020-01003-7</a>.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Probability Theory and Related Fields (2021).","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Edge Universality for Non-Hermitian Random Matrices.” <i>Probability Theory and Related Fields</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00440-020-01003-7\">https://doi.org/10.1007/s00440-020-01003-7</a>.","ama":"Cipolloni G, Erdös L, Schröder DJ. Edge universality for non-Hermitian random matrices. <i>Probability Theory and Related Fields</i>. 2021. doi:<a href=\"https://doi.org/10.1007/s00440-020-01003-7\">10.1007/s00440-020-01003-7</a>"},"title":"Edge universality for non-Hermitian random matrices","date_updated":"2026-04-02T14:03:52Z","abstract":[{"lang":"eng","text":"We consider large non-Hermitian real or complex random matrices X with independent, identically distributed centred entries. We prove that their local eigenvalue statistics near the spectral edge, the unit circle, coincide with those of the Ginibre ensemble, i.e. when the matrix elements of X are Gaussian. This result is the non-Hermitian counterpart of the universality of the Tracy–Widom distribution at the spectral edges of the Wigner ensemble."}],"author":[{"last_name":"Cipolloni","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio"},{"orcid":"0000-0001-5366-9603","full_name":"Erdös, László","first_name":"László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","first_name":"Dominik J","last_name":"Schröder","id":"408ED176-F248-11E8-B48F-1D18A9856A87"}],"article_processing_charge":"Yes (via OA deal)","year":"2021","date_created":"2020-10-04T22:01:37Z","oa":1,"external_id":{"isi":["000572724600002"],"arxiv":["1908.00969"]},"article_type":"original","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"ddc":["510"],"month":"02","isi":1,"scopus_import":"1","_id":"8601","oa_version":"Published Version","publication":"Probability Theory and Related Fields","language":[{"iso":"eng"}],"publication_status":"published","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","publisher":"Springer Nature","type":"journal_article","corr_author":"1","quality_controlled":"1","doi":"10.1007/s00440-020-01003-7","publication_identifier":{"issn":["0178-8051"],"eissn":["1432-2064"]},"file":[{"content_type":"application/pdf","date_created":"2020-10-05T14:53:40Z","relation":"main_file","success":1,"file_name":"2020_ProbTheory_Cipolloni.pdf","checksum":"611ae28d6055e1e298d53a57beb05ef4","file_size":497032,"file_id":"8612","access_level":"open_access","date_updated":"2020-10-05T14:53:40Z","creator":"dernst"}],"fulldoi":"https://doi.org/10.1007/s00440-020-01003-7","ec_funded":1,"department":[{"_id":"LaEr"}],"has_accepted_license":"1","date_published":"2021-02-01T00:00:00Z","file_date_updated":"2020-10-05T14:53:40Z","status":"public"},{"oa":1,"acknowledgement":"I gratefully acknowledge the financial support from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 665385 and my advisor’s ERC Advanced Grant No. 338804.","date_created":"2021-01-21T18:16:54Z","year":"2021","article_processing_charge":"No","author":[{"orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio","first_name":"Giorgio","last_name":"Cipolloni","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"}],"abstract":[{"text":"In the first part of the thesis we consider Hermitian random matrices. Firstly, we consider sample covariance matrices XX∗ with X having independent identically distributed (i.i.d.) centred entries. We prove a Central Limit Theorem for differences of linear statistics of XX∗ and its minor after removing the first column of X. Secondly, we consider Wigner-type matrices and prove that the eigenvalue statistics near cusp singularities of the limiting density of states are universal and that they form a Pearcey process. Since the limiting eigenvalue distribution admits only square root (edge) and cubic root (cusp) singularities, this concludes the third and last remaining case of the Wigner-Dyson-Mehta universality conjecture. The main technical ingredients are an optimal local law at the cusp, and the proof of the fast relaxation to equilibrium of the Dyson Brownian motion in the cusp regime.\r\nIn the second part we consider non-Hermitian matrices X with centred i.i.d. entries. We normalise the entries of X to have variance N −1. It is well known that the empirical eigenvalue density converges to the uniform distribution on the unit disk (circular law). In the first project, we prove universality of the local eigenvalue statistics close to the edge of the spectrum. This is the non-Hermitian analogue of the TracyWidom universality at the Hermitian edge. Technically we analyse the evolution of the spectral distribution of X along the Ornstein-Uhlenbeck flow for very long time\r\n(up to t = +∞). In the second project, we consider linear statistics of eigenvalues for macroscopic test functions f in the Sobolev space H2+ϵ and prove their convergence to the projection of the Gaussian Free Field on the unit disk. We prove this result for non-Hermitian matrices with real or complex entries. The main technical ingredients are: (i) local law for products of two resolvents at different spectral parameters, (ii) analysis of correlated Dyson Brownian motions.\r\nIn the third and final part we discuss the mathematically rigorous application of supersymmetric techniques (SUSY ) to give a lower tail estimate of the lowest singular value of X − z, with z ∈ C. More precisely, we use superbosonisation formula to give an integral representation of the resolvent of (X − z)(X − z)∗ which reduces to two and three contour integrals in the complex and real case, respectively. The rigorous analysis of these integrals is quite challenging since simple saddle point analysis cannot be applied (the main contribution comes from a non-trivial manifold). Our result\r\nimproves classical smoothing inequalities in the regime |z| ≈ 1; this result is essential to prove edge universality for i.i.d. non-Hermitian matrices.","lang":"eng"}],"date_updated":"2026-04-08T06:59:33Z","title":"Fluctuations in the spectrum of random matrices","project":[{"call_identifier":"H2020","grant_number":"665385","name":"International IST Doctoral Program","_id":"2564DBCA-B435-11E9-9278-68D0E5697425"},{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"citation":{"ama":"Cipolloni G. Fluctuations in the spectrum of random matrices. 2021. doi:<a href=\"https://doi.org/10.15479/AT:ISTA:9022\">10.15479/AT:ISTA:9022</a>","ista":"Cipolloni G. 2021. Fluctuations in the spectrum of random matrices. Institute of Science and Technology Austria.","ieee":"G. Cipolloni, “Fluctuations in the spectrum of random matrices,” Institute of Science and Technology Austria, 2021.","apa":"Cipolloni, G. (2021). <i>Fluctuations in the spectrum of random matrices</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/AT:ISTA:9022\">https://doi.org/10.15479/AT:ISTA:9022</a>","short":"G. Cipolloni, Fluctuations in the Spectrum of Random Matrices, Institute of Science and Technology Austria, 2021.","mla":"Cipolloni, Giorgio. <i>Fluctuations in the Spectrum of Random Matrices</i>. Institute of Science and Technology Austria, 2021, doi:<a href=\"https://doi.org/10.15479/AT:ISTA:9022\">10.15479/AT:ISTA:9022</a>.","chicago":"Cipolloni, Giorgio. “Fluctuations in the Spectrum of Random Matrices.” Institute of Science and Technology Austria, 2021. <a href=\"https://doi.org/10.15479/AT:ISTA:9022\">https://doi.org/10.15479/AT:ISTA:9022</a>."},"alternative_title":["ISTA Thesis"],"day":"25","status":"public","file_date_updated":"2021-01-25T14:19:10Z","degree_awarded":"PhD","date_published":"2021-01-25T00:00:00Z","has_accepted_license":"1","ec_funded":1,"OA_place":"publisher","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"fulldoi":"https://doi.org/10.15479/AT:ISTA:9022","doi":"10.15479/AT:ISTA:9022","publication_identifier":{"issn":["2663-337X"]},"file":[{"file_size":4127796,"checksum":"5a93658a5f19478372523ee232887e2b","file_name":"thesis.pdf","access_level":"open_access","creator":"gcipollo","date_updated":"2021-01-25T14:19:03Z","file_id":"9043","date_created":"2021-01-25T14:19:03Z","content_type":"application/pdf","success":1,"relation":"main_file"},{"checksum":"e8270eddfe6a988e92a53c88d1d19b8c","file_size":12775206,"file_name":"Thesis_files.zip","date_updated":"2021-01-25T14:19:10Z","creator":"gcipollo","access_level":"closed","file_id":"9044","date_created":"2021-01-25T14:19:10Z","content_type":"application/zip","relation":"source_file"}],"corr_author":"1","type":"dissertation","publisher":"Institute of Science and Technology Austria","supervisor":[{"last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","full_name":"Erdös, László","orcid":"0000-0001-5366-9603"}],"publication_status":"published","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","language":[{"iso":"eng"}],"page":"380","oa_version":"Published Version","_id":"9022","month":"01","ddc":["510"]},{"acknowledgement":"D. Virosztek was supported by the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 846294, and partially supported by the Hungarian National Research, Development and Innovation Office (NKFIH) via grants no. K124152, and no. KH129601.","oa":1,"external_id":{"isi":["000619676100035"],"arxiv":["1910.10447"]},"article_type":"original","article_processing_charge":"No","year":"2021","date_created":"2021-01-22T17:55:17Z","title":"The metric property of the quantum Jensen-Shannon divergence","date_updated":"2025-04-14T07:50:40Z","author":[{"last_name":"Virosztek","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","first_name":"Daniel","orcid":"0000-0003-1109-5511","full_name":"Virosztek, Daniel"}],"abstract":[{"lang":"eng","text":"In this short note, we prove that the square root of the quantum Jensen-Shannon divergence is a true metric on the cone of positive matrices, and hence in particular on the quantum state space."}],"arxiv":1,"article_number":"107595","day":"26","project":[{"call_identifier":"H2020","name":"Geometric study of Wasserstein spaces and free probability","_id":"26A455A6-B435-11E9-9278-68D0E5697425","grant_number":"846294"}],"intvolume":"       380","citation":{"ama":"Virosztek D. The metric property of the quantum Jensen-Shannon divergence. <i>Advances in Mathematics</i>. 2021;380(3). doi:<a href=\"https://doi.org/10.1016/j.aim.2021.107595\">10.1016/j.aim.2021.107595</a>","chicago":"Virosztek, Daniel. “The Metric Property of the Quantum Jensen-Shannon Divergence.” <i>Advances in Mathematics</i>. Elsevier, 2021. <a href=\"https://doi.org/10.1016/j.aim.2021.107595\">https://doi.org/10.1016/j.aim.2021.107595</a>.","short":"D. Virosztek, Advances in Mathematics 380 (2021).","mla":"Virosztek, Daniel. “The Metric Property of the Quantum Jensen-Shannon Divergence.” <i>Advances in Mathematics</i>, vol. 380, no. 3, 107595, Elsevier, 2021, doi:<a href=\"https://doi.org/10.1016/j.aim.2021.107595\">10.1016/j.aim.2021.107595</a>.","apa":"Virosztek, D. (2021). The metric property of the quantum Jensen-Shannon divergence. <i>Advances in Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.aim.2021.107595\">https://doi.org/10.1016/j.aim.2021.107595</a>","ieee":"D. Virosztek, “The metric property of the quantum Jensen-Shannon divergence,” <i>Advances in Mathematics</i>, vol. 380, no. 3. Elsevier, 2021.","ista":"Virosztek D. 2021. The metric property of the quantum Jensen-Shannon divergence. Advances in Mathematics. 380(3), 107595."},"volume":380,"date_published":"2021-03-26T00:00:00Z","status":"public","issue":"3","keyword":["General Mathematics"],"quality_controlled":"1","doi":"10.1016/j.aim.2021.107595","publication_identifier":{"issn":["0001-8708"]},"fulldoi":"https://doi.org/10.1016/j.aim.2021.107595","ec_funded":1,"department":[{"_id":"LaEr"}],"publication":"Advances in Mathematics","language":[{"iso":"eng"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication_status":"published","main_file_link":[{"url":"https://arxiv.org/abs/1910.10447","open_access":"1"}],"publisher":"Elsevier","type":"journal_article","month":"03","isi":1,"oa_version":"Preprint","_id":"9036","scopus_import":"1"},{"abstract":[{"lang":"eng","text":"We consider a model of the Riemann zeta function on the critical axis and study its maximum over intervals of length (log T)θ, where θ is either fixed or tends to zero at a suitable rate.\r\nIt is shown that the deterministic level of the maximum interpolates smoothly between the ones\r\nof log-correlated variables and of i.i.d. random variables, exhibiting a smooth transition ‘from\r\n3/4 to 1/4’ in the second order. This provides a natural context where extreme value statistics of\r\nlog-correlated variables with time-dependent variance and rate occur. A key ingredient of the\r\nproof is a precise upper tail tightness estimate for the maximum of the model on intervals of\r\nsize one, that includes a Gaussian correction. This correction is expected to be present for the\r\nRiemann zeta function and pertains to the question of the correct order of the maximum of\r\nthe zeta function in large intervals."}],"author":[{"full_name":"Arguin, Louis-Pierre","first_name":"Louis-Pierre","last_name":"Arguin"},{"full_name":"Dubach, Guillaume","orcid":"0000-0001-6892-8137","first_name":"Guillaume","id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E","last_name":"Dubach"},{"full_name":"Hartung, Lisa","first_name":"Lisa","last_name":"Hartung"}],"type":"preprint","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_status":"submitted","language":[{"iso":"eng"}],"title":"Maxima of a random model of the Riemann zeta function over intervals of varying length","publication":"arXiv","main_file_link":[{"url":"https://arxiv.org/abs/2103.04817","open_access":"1"}],"date_updated":"2025-04-14T07:43:51Z","day":"08","citation":{"ista":"Arguin L-P, Dubach G, Hartung L. Maxima of a random model of the Riemann zeta function over intervals of varying length. arXiv, 2103.04817.","ieee":"L.-P. Arguin, G. Dubach, and L. Hartung, “Maxima of a random model of the Riemann zeta function over intervals of varying length,” <i>arXiv</i>. .","apa":"Arguin, L.-P., Dubach, G., &#38; Hartung, L. (n.d.). Maxima of a random model of the Riemann zeta function over intervals of varying length. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2103.04817\">https://doi.org/10.48550/arXiv.2103.04817</a>","mla":"Arguin, Louis-Pierre, et al. “Maxima of a Random Model of the Riemann Zeta Function over Intervals of Varying Length.” <i>ArXiv</i>, 2103.04817, doi:<a href=\"https://doi.org/10.48550/arXiv.2103.04817\">10.48550/arXiv.2103.04817</a>.","short":"L.-P. Arguin, G. Dubach, L. Hartung, ArXiv (n.d.).","chicago":"Arguin, Louis-Pierre, Guillaume Dubach, and Lisa Hartung. “Maxima of a Random Model of the Riemann Zeta Function over Intervals of Varying Length.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2103.04817\">https://doi.org/10.48550/arXiv.2103.04817</a>.","ama":"Arguin L-P, Dubach G, Hartung L. Maxima of a random model of the Riemann zeta function over intervals of varying length. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2103.04817\">10.48550/arXiv.2103.04817</a>"},"project":[{"call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"}],"arxiv":1,"month":"03","_id":"9230","oa_version":"Preprint","article_number":"2103.04817","status":"public","acknowledgement":"The research of L.-P. A. is supported in part by the grant NSF CAREER DMS-1653602. G. D. gratefully acknowledges support from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411. The research of L. H. is supported in part by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through Project-ID 233630050 -TRR 146, Project-ID 443891315 within SPP 2265 and Project-ID 446173099.","date_published":"2021-03-08T00:00:00Z","external_id":{"arxiv":["2103.04817"]},"oa":1,"fulldoi":"https://doi.org/10.48550/arXiv.2103.04817","article_processing_charge":"No","year":"2021","date_created":"2021-03-09T11:08:15Z","department":[{"_id":"LaEr"}],"ec_funded":1,"doi":"10.48550/arXiv.2103.04817"},{"day":"21","project":[{"grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020"}],"citation":{"ama":"Dubach G, Mühlböck F. Formal verification of Zagier’s one-sentence proof. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2103.11389\">10.48550/arXiv.2103.11389</a>","ista":"Dubach G, Mühlböck F. Formal verification of Zagier’s one-sentence proof. arXiv, 2103.11389.","ieee":"G. Dubach and F. Mühlböck, “Formal verification of Zagier’s one-sentence proof,” <i>arXiv</i>. .","apa":"Dubach, G., &#38; Mühlböck, F. (n.d.). Formal verification of Zagier’s one-sentence proof. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2103.11389\">https://doi.org/10.48550/arXiv.2103.11389</a>","mla":"Dubach, Guillaume, and Fabian Mühlböck. “Formal Verification of Zagier’s One-Sentence Proof.” <i>ArXiv</i>, 2103.11389, doi:<a href=\"https://doi.org/10.48550/arXiv.2103.11389\">10.48550/arXiv.2103.11389</a>.","short":"G. Dubach, F. Mühlböck, ArXiv (n.d.).","chicago":"Dubach, Guillaume, and Fabian Mühlböck. “Formal Verification of Zagier’s One-Sentence Proof.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2103.11389\">https://doi.org/10.48550/arXiv.2103.11389</a>."},"arxiv":1,"article_number":"2103.11389","abstract":[{"lang":"eng","text":"We comment on two formal proofs of Fermat's sum of two squares theorem, written using the Mathematical Components libraries of the Coq proof assistant. The first one follows Zagier's celebrated one-sentence proof; the second follows David Christopher's recent new proof relying on partition-theoretic arguments. Both formal proofs rely on a general property of involutions of finite sets, of independent interest. The proof technique consists for the most part of automating recurrent tasks (such as case distinctions and computations on natural numbers) via ad hoc tactics."}],"author":[{"orcid":"0000-0001-6892-8137","full_name":"Dubach, Guillaume","id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E","last_name":"Dubach","first_name":"Guillaume"},{"orcid":"0000-0003-1548-0177","full_name":"Mühlböck, Fabian","first_name":"Fabian","id":"6395C5F6-89DF-11E9-9C97-6BDFE5697425","last_name":"Mühlböck"}],"title":"Formal verification of Zagier's one-sentence proof","date_updated":"2025-04-15T06:26:12Z","article_processing_charge":"No","date_created":"2021-03-23T05:38:48Z","year":"2021","oa":1,"external_id":{"arxiv":["2103.11389"]},"month":"03","_id":"9281","oa_version":"Preprint","type":"preprint","language":[{"iso":"eng"}],"publication":"arXiv","publication_status":"submitted","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","related_material":{"record":[{"id":"9946","relation":"other","status":"public"}]},"main_file_link":[{"url":"https://arxiv.org/abs/2103.11389","open_access":"1"}],"fulldoi":"https://doi.org/10.48550/arXiv.2103.11389","department":[{"_id":"LaEr"},{"_id":"ToHe"}],"ec_funded":1,"corr_author":"1","doi":"10.48550/arXiv.2103.11389","status":"public","date_published":"2021-03-21T00:00:00Z"},{"volume":26,"citation":{"ama":"Cipolloni G, Erdös L, Schröder DJ. Fluctuation around the circular law for random matrices with real entries. <i>Electronic Journal of Probability</i>. 2021;26. doi:<a href=\"https://doi.org/10.1214/21-EJP591\">10.1214/21-EJP591</a>","ista":"Cipolloni G, Erdös L, Schröder DJ. 2021. Fluctuation around the circular law for random matrices with real entries. Electronic Journal of Probability. 26, 24.","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2021). Fluctuation around the circular law for random matrices with real entries. <i>Electronic Journal of Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/21-EJP591\">https://doi.org/10.1214/21-EJP591</a>","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Fluctuation around the circular law for random matrices with real entries,” <i>Electronic Journal of Probability</i>, vol. 26. Institute of Mathematical Statistics, 2021.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Electronic Journal of Probability 26 (2021).","mla":"Cipolloni, Giorgio, et al. “Fluctuation around the Circular Law for Random Matrices with Real Entries.” <i>Electronic Journal of Probability</i>, vol. 26, 24, Institute of Mathematical Statistics, 2021, doi:<a href=\"https://doi.org/10.1214/21-EJP591\">10.1214/21-EJP591</a>.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Fluctuation around the Circular Law for Random Matrices with Real Entries.” <i>Electronic Journal of Probability</i>. Institute of Mathematical Statistics, 2021. <a href=\"https://doi.org/10.1214/21-EJP591\">https://doi.org/10.1214/21-EJP591</a>."},"project":[{"grant_number":"665385","name":"International IST Doctoral Program","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"intvolume":"        26","day":"23","article_number":"24","arxiv":1,"author":[{"last_name":"Cipolloni","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio","full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992"},{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös"},{"first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","last_name":"Schröder","full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856"}],"abstract":[{"lang":"eng","text":"We extend our recent result [22] on the central limit theorem for the linear eigenvalue statistics of non-Hermitian matrices X with independent, identically distributed complex entries to the real symmetry class. We find that the expectation and variance substantially differ from their complex counterparts, reflecting (i) the special spectral symmetry of real matrices onto the real axis; and (ii) the fact that real i.i.d. matrices have many real eigenvalues. Our result generalizes the previously known special cases where either the test function is analytic [49] or the first four moments of the matrix elements match the real Gaussian [59, 44]. The key element of the proof is the analysis of several weakly dependent Dyson Brownian motions (DBMs). The conceptual novelty of the real case compared with [22] is that the correlation structure of the stochastic differentials in each individual DBM is non-trivial, potentially even jeopardising its well-posedness."}],"date_updated":"2026-04-02T14:00:37Z","title":"Fluctuation around the circular law for random matrices with real entries","year":"2021","date_created":"2021-05-23T22:01:44Z","article_processing_charge":"No","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"external_id":{"arxiv":["2002.02438"],"isi":["000641855600001"]},"oa":1,"oa_version":"Published Version","_id":"9412","scopus_import":"1","isi":1,"month":"03","ddc":["510"],"type":"journal_article","publisher":"Institute of Mathematical Statistics","publication_status":"published","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","language":[{"iso":"eng"}],"publication":"Electronic Journal of Probability","department":[{"_id":"LaEr"}],"ec_funded":1,"fulldoi":"https://doi.org/10.1214/21-EJP591","publication_identifier":{"eissn":["1083-6489"]},"file":[{"content_type":"application/pdf","date_created":"2021-05-25T13:24:19Z","relation":"main_file","success":1,"file_name":"2021_EJP_Cipolloni.pdf","file_size":865148,"checksum":"864ab003ad4cffea783f65aa8c2ba69f","file_id":"9423","access_level":"open_access","date_updated":"2021-05-25T13:24:19Z","creator":"kschuh"}],"doi":"10.1214/21-EJP591","quality_controlled":"1","status":"public","file_date_updated":"2021-05-25T13:24:19Z","date_published":"2021-03-23T00:00:00Z","has_accepted_license":"1"},{"acknowledgement":"The first author is supported in part by Hong Kong RGC Grant GRF 16301519 and NSFC 11871425. The second author is supported in part by ERC Advanced Grant RANMAT 338804. The third author is supported in part by Swedish Research Council Grant VR-2017-05195 and the Knut and Alice Wallenberg Foundation","oa":1,"external_id":{"isi":["000654960800001"],"arxiv":["2008.07061"]},"article_type":"original","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"article_processing_charge":"No","year":"2021","date_created":"2021-06-13T22:01:33Z","title":"Equipartition principle for Wigner matrices","date_updated":"2026-04-07T08:36:39Z","abstract":[{"text":"We prove that the energy of any eigenvector of a sum of several independent large Wigner matrices is equally distributed among these matrices with very high precision. This shows a particularly strong microcanonical form of the equipartition principle for quantum systems whose components are modelled by Wigner matrices. ","lang":"eng"}],"author":[{"first_name":"Zhigang","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87","last_name":"Bao","orcid":"0000-0003-3036-1475","full_name":"Bao, Zhigang"},{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László"},{"id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","last_name":"Schnelli","first_name":"Kevin","orcid":"0000-0003-0954-3231","full_name":"Schnelli, Kevin"}],"arxiv":1,"article_number":"e44","day":"27","citation":{"ama":"Bao Z, Erdös L, Schnelli K. Equipartition principle for Wigner matrices. <i>Forum of Mathematics, Sigma</i>. 2021;9. doi:<a href=\"https://doi.org/10.1017/fms.2021.38\">10.1017/fms.2021.38</a>","short":"Z. Bao, L. Erdös, K. Schnelli, Forum of Mathematics, Sigma 9 (2021).","mla":"Bao, Zhigang, et al. “Equipartition Principle for Wigner Matrices.” <i>Forum of Mathematics, Sigma</i>, vol. 9, e44, Cambridge University Press, 2021, doi:<a href=\"https://doi.org/10.1017/fms.2021.38\">10.1017/fms.2021.38</a>.","chicago":"Bao, Zhigang, László Erdös, and Kevin Schnelli. “Equipartition Principle for Wigner Matrices.” <i>Forum of Mathematics, Sigma</i>. Cambridge University Press, 2021. <a href=\"https://doi.org/10.1017/fms.2021.38\">https://doi.org/10.1017/fms.2021.38</a>.","ista":"Bao Z, Erdös L, Schnelli K. 2021. Equipartition principle for Wigner matrices. Forum of Mathematics, Sigma. 9, e44.","apa":"Bao, Z., Erdös, L., &#38; Schnelli, K. (2021). Equipartition principle for Wigner matrices. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fms.2021.38\">https://doi.org/10.1017/fms.2021.38</a>","ieee":"Z. Bao, L. Erdös, and K. Schnelli, “Equipartition principle for Wigner matrices,” <i>Forum of Mathematics, Sigma</i>, vol. 9. Cambridge University Press, 2021."},"intvolume":"         9","project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"volume":9,"has_accepted_license":"1","date_published":"2021-05-27T00:00:00Z","status":"public","file_date_updated":"2021-06-15T14:40:45Z","quality_controlled":"1","doi":"10.1017/fms.2021.38","publication_identifier":{"eissn":["2050-5094"]},"file":[{"success":1,"relation":"main_file","date_created":"2021-06-15T14:40:45Z","content_type":"application/pdf","access_level":"open_access","creator":"cziletti","date_updated":"2021-06-15T14:40:45Z","file_id":"9555","checksum":"47c986578de132200d41e6d391905519","file_size":483458,"file_name":"2021_ForumMath_Bao.pdf"}],"fulldoi":"https://doi.org/10.1017/fms.2021.38","department":[{"_id":"LaEr"}],"ec_funded":1,"language":[{"iso":"eng"}],"publication":"Forum of Mathematics, Sigma","publication_status":"published","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","publisher":"Cambridge University Press","type":"journal_article","ddc":["510"],"month":"05","isi":1,"oa_version":"Published Version","_id":"9550","scopus_import":"1"}]