[{"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"}],"publication_status":"published","title":"Thermalisation for Wigner matrices","oa_version":"Published Version","file_date_updated":"2022-07-29T07:22:08Z","quality_controlled":"1","intvolume":"       282","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.","volume":282,"publication_identifier":{"eissn":["1096-0783"],"issn":["0022-1236"]},"article_type":"original","doi":"10.1016/j.jfa.2022.109394","date_created":"2022-02-06T23:01:30Z","author":[{"first_name":"Giorgio","orcid":"0000-0002-4901-7992","last_name":"Cipolloni","full_name":"Cipolloni, Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0001-5366-9603","last_name":"Erdös","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László"},{"orcid":"0000-0002-2904-1856","last_name":"Schröder","first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","full_name":"Schröder, Dominik J"}],"_id":"10732","scopus_import":"1","date_published":"2022-04-15T00:00:00Z","oa":1,"citation":{"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.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Journal of Functional Analysis 282 (2022).","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>","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>"},"arxiv":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","language":[{"iso":"eng"}],"ddc":["500"],"date_updated":"2024-10-09T21:01:33Z","file":[{"content_type":"application/pdf","file_size":652573,"date_updated":"2022-07-29T07:22:08Z","success":1,"relation":"main_file","file_id":"11690","date_created":"2022-07-29T07:22:08Z","file_name":"2022_JourFunctionalAnalysis_Cipolloni.pdf","checksum":"b75fdad606ab507dc61109e0907d86c0","access_level":"open_access","creator":"dernst"}],"external_id":{"arxiv":["2102.09975"],"isi":["000781239100004"]},"article_number":"109394","status":"public","article_processing_charge":"Yes (via OA deal)","publication":"Journal of Functional Analysis","has_accepted_license":"1","department":[{"_id":"LaEr"}],"isi":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"type":"journal_article","year":"2022","publisher":"Elsevier","corr_author":"1","month":"04","issue":"8","day":"15"},{"pmid":1,"abstract":[{"lang":"eng","text":"We show that the fluctuations of the largest eigenvalue of a real symmetric or complex Hermitian Wigner matrix of size N converge to the Tracy–Widom laws at a rate O(N^{-1/3+\\omega }), as N tends to infinity. For Wigner matrices this improves the previous rate O(N^{-2/9+\\omega }) obtained by Bourgade (J Eur Math Soc, 2021) for generalized Wigner matrices. Our result follows from a Green function comparison theorem, originally introduced by Erdős et al. (Adv Math 229(3):1435–1515, 2012) to prove edge universality, on a finer spectral parameter scale with improved error estimates. The proof relies on the continuous Green function flow induced by a matrix-valued Ornstein–Uhlenbeck process. Precise estimates on leading contributions from the third and fourth order moments of the matrix entries are obtained using iterative cumulant expansions and recursive comparisons for correlation functions, along with uniform convergence estimates for correlation kernels of the Gaussian invariant ensembles."}],"publication_status":"published","oa_version":"Published Version","title":"Convergence rate to the Tracy–Widom laws for the largest Eigenvalue of Wigner matrices","page":"839-907","file_date_updated":"2022-08-05T06:01:13Z","quality_controlled":"1","intvolume":"       393","acknowledgement":"Kevin Schnelli is supported in parts by the Swedish Research Council Grant VR-2017-05195, and the Knut and Alice Wallenberg Foundation. Yuanyuan Xu is supported by the Swedish Research Council Grant VR-2017-05195 and the ERC Advanced Grant “RMTBeyond” No. 101020331.","volume":393,"publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"article_type":"original","author":[{"orcid":"0000-0003-0954-3231","last_name":"Schnelli","first_name":"Kevin","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","full_name":"Schnelli, Kevin"},{"first_name":"Yuanyuan","orcid":"0000-0003-1559-1205","last_name":"Xu","full_name":"Xu, Yuanyuan","id":"7902bdb1-a2a4-11eb-a164-c9216f71aea3"}],"doi":"10.1007/s00220-022-04377-y","date_created":"2022-04-24T22:01:44Z","_id":"11332","scopus_import":"1","date_published":"2022-07-01T00:00:00Z","oa":1,"citation":{"ieee":"K. Schnelli and Y. Xu, “Convergence rate to the Tracy–Widom laws for the largest Eigenvalue of Wigner matrices,” <i>Communications in Mathematical Physics</i>, vol. 393. Springer Nature, pp. 839–907, 2022.","ista":"Schnelli K, Xu Y. 2022. Convergence rate to the Tracy–Widom laws for the largest Eigenvalue of Wigner matrices. Communications in Mathematical Physics. 393, 839–907.","apa":"Schnelli, K., &#38; Xu, Y. (2022). Convergence rate to the Tracy–Widom laws for the largest Eigenvalue of Wigner matrices. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-022-04377-y\">https://doi.org/10.1007/s00220-022-04377-y</a>","mla":"Schnelli, Kevin, and Yuanyuan Xu. “Convergence Rate to the Tracy–Widom Laws for the Largest Eigenvalue of Wigner Matrices.” <i>Communications in Mathematical Physics</i>, vol. 393, Springer Nature, 2022, pp. 839–907, doi:<a href=\"https://doi.org/10.1007/s00220-022-04377-y\">10.1007/s00220-022-04377-y</a>.","short":"K. Schnelli, Y. Xu, Communications in Mathematical Physics 393 (2022) 839–907.","chicago":"Schnelli, Kevin, and Yuanyuan Xu. “Convergence Rate to the Tracy–Widom Laws for the Largest Eigenvalue of Wigner Matrices.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s00220-022-04377-y\">https://doi.org/10.1007/s00220-022-04377-y</a>.","ama":"Schnelli K, Xu Y. Convergence rate to the Tracy–Widom laws for the largest Eigenvalue of Wigner matrices. <i>Communications in Mathematical Physics</i>. 2022;393:839-907. doi:<a href=\"https://doi.org/10.1007/s00220-022-04377-y\">10.1007/s00220-022-04377-y</a>"},"arxiv":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","language":[{"iso":"eng"}],"file":[{"content_type":"application/pdf","file_size":1141462,"date_updated":"2022-08-05T06:01:13Z","success":1,"relation":"main_file","date_created":"2022-08-05T06:01:13Z","file_name":"2022_CommunMathPhys_Schnelli.pdf","file_id":"11726","checksum":"bee0278c5efa9a33d9a2dc8d354a6c51","creator":"dernst","access_level":"open_access"}],"date_updated":"2025-06-11T14:01:05Z","ddc":["510"],"external_id":{"pmid":["35765414"],"isi":["000782737200001"],"arxiv":["2102.04330"]},"status":"public","article_processing_charge":"No","publication":"Communications in Mathematical Physics","department":[{"_id":"LaEr"}],"isi":1,"has_accepted_license":"1","ec_funded":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"project":[{"grant_number":"101020331","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"type":"journal_article","year":"2022","publisher":"Springer Nature","month":"07","day":"01"},{"_id":"11418","scopus_import":"1","author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio","last_name":"Cipolloni","orcid":"0000-0002-4901-7992","first_name":"Giorgio"},{"full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","orcid":"0000-0001-5366-9603","last_name":"Erdös"},{"last_name":"Schröder","orcid":"0000-0002-2904-1856","first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","full_name":"Schröder, Dominik J"}],"doi":"10.1214/21-AOP1552","date_created":"2022-05-29T22:01:53Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","date_published":"2022-05-01T00:00:00Z","oa":1,"citation":{"ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Normal fluctuation in quantum ergodicity for Wigner matrices. Annals of Probability. 50(3), 984–1012.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Normal fluctuation in quantum ergodicity for Wigner matrices,” <i>Annals of Probability</i>, vol. 50, no. 3. Institute of Mathematical Statistics, pp. 984–1012, 2022.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Annals of Probability 50 (2022) 984–1012.","mla":"Cipolloni, Giorgio, et al. “Normal Fluctuation in Quantum Ergodicity for Wigner Matrices.” <i>Annals of Probability</i>, vol. 50, no. 3, Institute of Mathematical Statistics, 2022, pp. 984–1012, doi:<a href=\"https://doi.org/10.1214/21-AOP1552\">10.1214/21-AOP1552</a>.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Normal Fluctuation in Quantum Ergodicity for Wigner Matrices.” <i>Annals of Probability</i>. Institute of Mathematical Statistics, 2022. <a href=\"https://doi.org/10.1214/21-AOP1552\">https://doi.org/10.1214/21-AOP1552</a>.","ama":"Cipolloni G, Erdös L, Schröder DJ. Normal fluctuation in quantum ergodicity for Wigner matrices. <i>Annals of Probability</i>. 2022;50(3):984-1012. doi:<a href=\"https://doi.org/10.1214/21-AOP1552\">10.1214/21-AOP1552</a>","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2022). Normal fluctuation in quantum ergodicity for Wigner matrices. <i>Annals of Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/21-AOP1552\">https://doi.org/10.1214/21-AOP1552</a>"},"arxiv":1,"intvolume":"        50","acknowledgement":"L.E. would like to thank Zhigang Bao for many illuminating discussions in an early stage of this research. The authors are also grateful to Paul Bourgade for his comments on the manuscript and the anonymous referee for several useful suggestions.","volume":50,"publication_identifier":{"eissn":["2168-894X"],"issn":["0091-1798"]},"article_type":"original","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2103.06730"}],"page":"984-1012","quality_controlled":"1","abstract":[{"lang":"eng","text":"We consider the quadratic form of a general high-rank deterministic matrix on the eigenvectors of an N×N\r\nWigner matrix and prove that it has Gaussian fluctuation for each bulk eigenvector in the large N limit. The proof is a combination of the energy method for the Dyson Brownian motion inspired by Marcinek and Yau (2021) and our recent multiresolvent local laws (Comm. Math. Phys. 388 (2021) 1005–1048)."}],"oa_version":"Preprint","title":"Normal fluctuation in quantum ergodicity for Wigner matrices","publication_status":"published","month":"05","publisher":"Institute of Mathematical Statistics","day":"01","issue":"3","year":"2022","type":"journal_article","status":"public","external_id":{"isi":["000793963400005"],"arxiv":["2103.06730"]},"publication":"Annals of Probability","isi":1,"department":[{"_id":"LaEr"}],"article_processing_charge":"No","language":[{"iso":"eng"}],"date_updated":"2023-08-03T07:16:53Z"},{"date_updated":"2026-04-07T12:37:10Z","ddc":["514"],"file":[{"content_type":"application/pdf","date_updated":"2022-01-14T07:27:45Z","file_size":505804,"success":1,"date_created":"2022-01-14T07:27:45Z","checksum":"d44f8123a52592a75b2c3b8ee2cd2435","file_name":"2022_MathPhyAnalGeo_Henheik.pdf","file_id":"10624","creator":"cchlebak","access_level":"open_access","relation":"main_file"}],"language":[{"iso":"eng"}],"related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"19540"}]},"has_accepted_license":"1","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"isi":1,"publication":"Mathematical Physics, Analysis and Geometry","article_processing_charge":"Yes (via OA deal)","status":"public","article_number":"3","external_id":{"arxiv":["2106.02015"],"isi":["000741387600001"]},"year":"2022","type":"journal_article","project":[{"grant_number":"101020331","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"keyword":["geometry and topology","mathematical physics"],"ec_funded":1,"issue":"1","day":"11","month":"01","corr_author":"1","publisher":"Springer Nature","title":"The BCS critical temperature at high density","oa_version":"Published Version","publication_status":"published","abstract":[{"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.","lang":"eng"}],"quality_controlled":"1","file_date_updated":"2022-01-14T07:27:45Z","article_type":"original","volume":25,"publication_identifier":{"eissn":["1572-9656"],"issn":["1385-0172"]},"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.","intvolume":"        25","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","arxiv":1,"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>","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>","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>.","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>.","short":"S.J. Henheik, Mathematical Physics, Analysis and Geometry 25 (2022).","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."},"oa":1,"date_published":"2022-01-11T00:00:00Z","scopus_import":"1","_id":"10623","author":[{"first_name":"Sven Joscha","orcid":"0000-0003-1106-327X","last_name":"Henheik","full_name":"Henheik, Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb"}],"date_created":"2022-01-13T15:40:53Z","doi":"10.1007/s11040-021-09415-0"},{"article_processing_charge":"No","publication":"Journal of Mathematical Physics","has_accepted_license":"1","isi":1,"department":[{"_id":"LaEr"}],"external_id":{"isi":["000905776200001"],"arxiv":["2208.12220"]},"article_number":"121101","status":"public","date_updated":"2026-04-07T12:37:10Z","file":[{"success":1,"date_updated":"2023-01-27T07:10:52Z","file_size":5251092,"content_type":"application/pdf","relation":"main_file","creator":"dernst","access_level":"open_access","file_name":"2022_JourMathPhysics_Henheik2.pdf","checksum":"213b93750080460718c050e4967cfdb4","file_id":"12410","date_created":"2023-01-27T07:10:52Z"}],"ddc":["510"],"related_material":{"record":[{"relation":"dissertation_contains","id":"19540","status":"public"}]},"language":[{"iso":"eng"}],"day":"01","issue":"12","publisher":"AIP Publishing","corr_author":"1","month":"12","type":"journal_article","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"year":"2022","ec_funded":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"file_date_updated":"2023-01-27T07:10:52Z","quality_controlled":"1","publication_status":"published","oa_version":"Published Version","title":"On adiabatic theory for extended fermionic lattice systems","abstract":[{"lang":"eng","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."}],"date_published":"2022-12-01T00:00:00Z","oa":1,"citation":{"ista":"Henheik SJ, Wessel T. 2022. On adiabatic theory for extended fermionic lattice systems. Journal of Mathematical Physics. 63(12), 121101.","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.","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>.","short":"S.J. Henheik, T. Wessel, Journal of Mathematical Physics 63 (2022).","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>.","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>","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>"},"arxiv":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","date_created":"2023-01-15T23:00:52Z","doi":"10.1063/5.0123441","author":[{"first_name":"Sven Joscha","last_name":"Henheik","orcid":"0000-0003-1106-327X","full_name":"Henheik, Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb"},{"full_name":"Wessel, Tom","first_name":"Tom","last_name":"Wessel"}],"_id":"12184","scopus_import":"1","publication_identifier":{"issn":["0022-2488"]},"volume":63,"article_type":"original","intvolume":"        63","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.\" "},{"ec_funded":1,"keyword":["mathematical physics","statistical and nonlinear physics"],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"type":"journal_article","year":"2022","publisher":"Springer Nature","month":"01","day":"18","issue":"1","related_material":{"record":[{"status":"public","id":"19540","relation":"dissertation_contains"}]},"language":[{"iso":"eng"}],"file":[{"content_type":"application/pdf","date_updated":"2022-01-19T09:41:14Z","file_size":357547,"success":1,"relation":"main_file","file_name":"2022_LettersMathPhys_Henheik.pdf","file_id":"10647","checksum":"7e8e69b76e892c305071a4736131fe18","date_created":"2022-01-19T09:41:14Z","creator":"cchlebak","access_level":"open_access"}],"date_updated":"2026-04-07T12:37:10Z","ddc":["530"],"external_id":{"pmid":["35125630"],"isi":["000744930400001"],"arxiv":["2106.13780"]},"article_number":"9","status":"public","article_processing_charge":"No","publication":"Letters in Mathematical Physics","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"isi":1,"has_accepted_license":"1","intvolume":"       112","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.","volume":112,"publication_identifier":{"issn":["0377-9017"],"eissn":["1573-0530"]},"article_type":"original","author":[{"id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","full_name":"Henheik, Sven Joscha","last_name":"Henheik","orcid":"0000-0003-1106-327X","first_name":"Sven Joscha"},{"full_name":"Teufel, Stefan","first_name":"Stefan","last_name":"Teufel"},{"last_name":"Wessel","first_name":"Tom","full_name":"Wessel, Tom"}],"doi":"10.1007/s11005-021-01494-y","date_created":"2022-01-18T16:18:25Z","_id":"10642","scopus_import":"1","date_published":"2022-01-18T00:00:00Z","oa":1,"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).","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>.","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>.","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>","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."},"arxiv":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","pmid":1,"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."}],"publication_status":"published","oa_version":"Published Version","title":"Local stability of ground states in locally gapped and weakly interacting quantum spin systems","quality_controlled":"1","file_date_updated":"2022-01-19T09:41:14Z"},{"article_processing_charge":"Yes (via OA deal)","publication":"Journal of Statistical Physics","isi":1,"department":[{"_id":"GradSch"},{"_id":"LaEr"},{"_id":"RoSe"}],"has_accepted_license":"1","external_id":{"isi":["000833007200002"]},"article_number":"5","status":"public","file":[{"file_size":419563,"date_updated":"2022-08-08T07:36:34Z","content_type":"application/pdf","success":1,"file_name":"2022_JourStatisticalPhysics_Henheik.pdf","file_id":"11746","checksum":"b398c4dbf65f71d417981d6e366427e9","date_created":"2022-08-08T07:36:34Z","access_level":"open_access","creator":"dernst","relation":"main_file"}],"ddc":["530"],"date_updated":"2026-04-07T13:01:40Z","related_material":{"record":[{"id":"19540","status":"public","relation":"dissertation_contains"},{"relation":"dissertation_contains","status":"public","id":"18135"}]},"language":[{"iso":"eng"}],"day":"29","publisher":"Springer Nature","corr_author":"1","month":"07","type":"journal_article","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331"}],"year":"2022","ec_funded":1,"keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"file_date_updated":"2022-08-08T07:36:34Z","quality_controlled":"1","publication_status":"published","title":"The BCS energy gap at high density","oa_version":"Published Version","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"}],"date_published":"2022-07-29T00:00:00Z","oa":1,"citation":{"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.","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>","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>","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>.","short":"S.J. Henheik, A.B. Lauritsen, Journal of Statistical Physics 189 (2022).","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>."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","doi":"10.1007/s10955-022-02965-9","author":[{"orcid":"0000-0003-1106-327X","last_name":"Henheik","first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","full_name":"Henheik, Sven Joscha"},{"full_name":"Lauritsen, Asbjørn Bækgaard","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1","first_name":"Asbjørn Bækgaard","orcid":"0000-0003-4476-2288","last_name":"Lauritsen"}],"date_created":"2022-08-05T11:36:56Z","_id":"11732","scopus_import":"1","volume":189,"publication_identifier":{"eissn":["1572-9613"],"issn":["0022-4715"]},"article_type":"original","intvolume":"       189","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)"},{"volume":11,"publication_identifier":{"eissn":["2010-3271"],"issn":["2010-3263"]},"article_type":"original","intvolume":"        11","oa":1,"date_published":"2022-10-01T00:00:00Z","citation":{"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.","ista":"Reker J. 2022. On the operator norm of a Hermitian random matrix with correlated entries. Random Matrices: Theory and Applications. 11(4), 2250036.","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>","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>.","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>"},"arxiv":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"first_name":"Jana","last_name":"Reker","full_name":"Reker, Jana","id":"e796e4f9-dc8d-11ea-abe3-97e26a0323e9"}],"date_created":"2022-04-08T07:11:12Z","doi":"10.1142/s2010326322500368","_id":"11135","scopus_import":"1","publication_status":"published","oa_version":"Preprint","title":"On the operator norm of a Hermitian random matrix with correlated entries","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"}],"quality_controlled":"1","main_file_link":[{"url":" https://doi.org/10.48550/arXiv.2103.03906","open_access":"1"}],"type":"journal_article","year":"2022","keyword":["Discrete Mathematics and Combinatorics","Statistics","Probability and Uncertainty","Statistics and Probability","Algebra and Number Theory"],"issue":"4","day":"01","publisher":"World Scientific Publishing","corr_author":"1","month":"10","date_updated":"2026-04-07T13:02:12Z","related_material":{"record":[{"id":"17164","status":"public","relation":"dissertation_contains"}]},"language":[{"iso":"eng"}],"article_processing_charge":"No","publication":"Random Matrices: Theory and Applications","isi":1,"department":[{"_id":"GradSch"},{"_id":"LaEr"}],"external_id":{"isi":["000848873800001"],"arxiv":["2103.03906"]},"article_number":"2250036","status":"public"},{"quality_controlled":"1","page":"221-280","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1907.13631"}],"publication_status":"published","title":"Spectral radius of random matrices with independent entries","oa_version":"Preprint","abstract":[{"lang":"eng","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."}],"arxiv":1,"citation":{"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.","ista":"Alt J, Erdös L, Krüger TH. 2021. Spectral radius of random matrices with independent entries. Probability and Mathematical Physics. 2(2), 221–280.","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>","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>.","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.","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>"},"date_published":"2021-05-21T00:00:00Z","oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","doi":"10.2140/pmp.2021.2.221","date_created":"2024-02-18T23:01:03Z","author":[{"last_name":"Alt","first_name":"Johannes","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87","full_name":"Alt, Johannes"},{"full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","last_name":"Erdös","orcid":"0000-0001-5366-9603"},{"first_name":"Torben H","last_name":"Krüger","orcid":"0000-0002-4821-3297","full_name":"Krüger, Torben H","id":"3020C786-F248-11E8-B48F-1D18A9856A87"}],"scopus_import":"1","_id":"15013","article_type":"original","publication_identifier":{"issn":["2690-0998"],"eissn":["2690-1005"]},"volume":2,"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.","intvolume":"         2","article_processing_charge":"No","department":[{"_id":"LaEr"}],"publication":"Probability and Mathematical Physics","external_id":{"arxiv":["1907.13631"]},"status":"public","date_updated":"2025-04-15T08:05:02Z","language":[{"iso":"eng"}],"day":"21","issue":"2","publisher":"Mathematical Sciences Publishers","month":"05","corr_author":"1","project":[{"grant_number":"338804","call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"type":"journal_article","year":"2021","ec_funded":1},{"date_updated":"2025-09-10T10:13:20Z","language":[{"iso":"eng"}],"article_processing_charge":"No","publication":"The Annals of Probability","department":[{"_id":"LaEr"}],"isi":1,"external_id":{"arxiv":["1904.04312"],"isi":["000681349000008"]},"status":"public","type":"journal_article","project":[{"name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"year":"2021","ec_funded":1,"keyword":["Statistics","Probability and Uncertainty","Statistics and Probability"],"issue":"4","day":"01","publisher":"Institute of Mathematical Statistics","corr_author":"1","month":"07","publication_status":"published","title":"On words of non-Hermitian random matrices","oa_version":"Preprint","abstract":[{"lang":"eng","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."}],"quality_controlled":"1","page":"1886-1916","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1904.04312","open_access":"1"}],"volume":49,"publication_identifier":{"issn":["0091-1798"]},"article_type":"original","intvolume":"        49","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.","date_published":"2021-07-01T00:00:00Z","oa":1,"arxiv":1,"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>","short":"G. Dubach, Y. Peled, The Annals of Probability 49 (2021) 1886–1916.","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>.","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>.","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>","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."},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","author":[{"last_name":"Dubach","orcid":"0000-0001-6892-8137","first_name":"Guillaume","id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E","full_name":"Dubach, Guillaume"},{"full_name":"Peled, Yuval","last_name":"Peled","first_name":"Yuval"}],"doi":"10.1214/20-aop1496","date_created":"2024-04-03T07:19:42Z","_id":"15259","scopus_import":"1"},{"intvolume":"       388","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria).","volume":388,"publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"article_type":"original","author":[{"full_name":"Cipolloni, Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio","orcid":"0000-0002-4901-7992","last_name":"Cipolloni"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös","first_name":"László"},{"first_name":"Dominik J","last_name":"Schröder","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87"}],"doi":"10.1007/s00220-021-04239-z","date_created":"2021-11-07T23:01:25Z","_id":"10221","scopus_import":"1","oa":1,"date_published":"2021-10-29T00:00:00Z","citation":{"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.","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>","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>.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Communications in Mathematical Physics 388 (2021) 1005–1048.","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>"},"arxiv":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","abstract":[{"lang":"eng","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)."}],"publication_status":"published","oa_version":"Published Version","title":"Eigenstate thermalization hypothesis for Wigner matrices","page":"1005–1048","quality_controlled":"1","file_date_updated":"2022-02-02T10:19:55Z","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"type":"journal_article","year":"2021","publisher":"Springer Nature","corr_author":"1","month":"10","day":"29","issue":"2","language":[{"iso":"eng"}],"ddc":["510"],"date_updated":"2025-04-15T06:53:08Z","file":[{"relation":"main_file","access_level":"open_access","creator":"cchlebak","file_id":"10715","date_created":"2022-02-02T10:19:55Z","file_name":"2021_CommunMathPhys_Cipolloni.pdf","checksum":"a2c7b6f5d23b5453cd70d1261272283b","success":1,"content_type":"application/pdf","date_updated":"2022-02-02T10:19:55Z","file_size":841426}],"external_id":{"isi":["000712232700001"],"arxiv":["2012.13215"]},"status":"public","article_processing_charge":"Yes (via OA deal)","publication":"Communications in Mathematical Physics","department":[{"_id":"LaEr"}],"has_accepted_license":"1","isi":1},{"language":[{"iso":"eng"}],"file":[{"success":1,"date_updated":"2021-11-15T10:10:17Z","file_size":735940,"content_type":"application/pdf","access_level":"open_access","creator":"cchlebak","checksum":"1c975afb31460277ce4d22b93538e5f9","file_name":"2021_ElecJournalProb_Dubach.pdf","file_id":"10288","date_created":"2021-11-15T10:10:17Z","relation":"main_file"}],"date_updated":"2025-04-14T07:43:47Z","ddc":["519"],"status":"public","article_number":"124","publication":"Electronic Journal of Probability","has_accepted_license":"1","department":[{"_id":"LaEr"}],"article_processing_charge":"No","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"ec_funded":1,"year":"2021","project":[{"grant_number":"754411","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"type":"journal_article","month":"09","publisher":"Institute of Mathematical Statistics","day":"28","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."}],"title":"On eigenvector statistics in the spherical and truncated unitary ensembles","oa_version":"Published Version","publication_status":"published","file_date_updated":"2021-11-15T10:10:17Z","quality_controlled":"1","intvolume":"        26","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.","volume":26,"publication_identifier":{"eissn":["1083-6489"]},"article_type":"original","_id":"10285","scopus_import":"1","date_created":"2021-11-14T23:01:25Z","author":[{"full_name":"Dubach, Guillaume","id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E","first_name":"Guillaume","last_name":"Dubach","orcid":"0000-0001-6892-8137"}],"doi":"10.1214/21-EJP686","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","date_published":"2021-09-28T00:00:00Z","oa":1,"citation":{"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>.","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>","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>","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."}},{"page":"203-217","main_file_link":[{"url":"https://arxiv.org/abs/2002.11678","open_access":"1"}],"quality_controlled":"1","abstract":[{"lang":"eng","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."}],"publication_status":"published","oa_version":"Preprint","title":"A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means","doi":"10.1016/j.laa.2020.09.007","author":[{"first_name":"József","last_name":"Pitrik","full_name":"Pitrik, József"},{"id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","full_name":"Virosztek, Daniel","orcid":"0000-0003-1109-5511","last_name":"Virosztek","first_name":"Daniel"}],"date_created":"2020-09-11T08:35:50Z","scopus_import":"1","_id":"8373","arxiv":1,"citation":{"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.","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>.","short":"J. Pitrik, D. Virosztek, Linear Algebra and Its Applications 609 (2021) 203–217.","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>.","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>","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>"},"date_published":"2021-01-15T00:00:00Z","oa":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","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.","intvolume":"       609","article_type":"original","publication_identifier":{"issn":["0024-3795"]},"volume":609,"external_id":{"isi":["000581730500011"],"arxiv":["2002.11678"]},"status":"public","article_processing_charge":"No","department":[{"_id":"LaEr"}],"isi":1,"publication":"Linear Algebra and its Applications","language":[{"iso":"eng"}],"date_updated":"2025-04-14T07:50:40Z","publisher":"Elsevier","month":"01","day":"15","ec_funded":1,"keyword":["Kubo-Ando mean","weighted multivariate mean","barycenter"],"type":"journal_article","project":[{"_id":"26A455A6-B435-11E9-9278-68D0E5697425","name":"Geometric study of Wasserstein spaces and free probability","call_identifier":"H2020","grant_number":"846294"},{"_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme","grant_number":"291734"}],"year":"2021"},{"main_file_link":[{"url":"https://arxiv.org/abs/1910.10447","open_access":"1"}],"quality_controlled":"1","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."}],"publication_status":"published","title":"The metric property of the quantum Jensen-Shannon divergence","oa_version":"Preprint","doi":"10.1016/j.aim.2021.107595","author":[{"orcid":"0000-0003-1109-5511","last_name":"Virosztek","first_name":"Daniel","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","full_name":"Virosztek, Daniel"}],"date_created":"2021-01-22T17:55:17Z","_id":"9036","scopus_import":"1","oa":1,"date_published":"2021-03-26T00:00:00Z","arxiv":1,"citation":{"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>","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>.","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>.","short":"D. Virosztek, Advances in Mathematics 380 (2021).","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>","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."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","intvolume":"       380","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.","publication_identifier":{"issn":["0001-8708"]},"volume":380,"article_type":"original","external_id":{"arxiv":["1910.10447"],"isi":["000619676100035"]},"article_number":"107595","status":"public","article_processing_charge":"No","publication":"Advances in Mathematics","department":[{"_id":"LaEr"}],"isi":1,"language":[{"iso":"eng"}],"date_updated":"2025-04-14T07:50:40Z","publisher":"Elsevier","month":"03","issue":"3","day":"26","ec_funded":1,"keyword":["General Mathematics"],"project":[{"_id":"26A455A6-B435-11E9-9278-68D0E5697425","name":"Geometric study of Wasserstein spaces and free probability","call_identifier":"H2020","grant_number":"846294"}],"type":"journal_article","year":"2021"},{"article_number":"2103.04817","external_id":{"arxiv":["2103.04817"]},"main_file_link":[{"url":"https://arxiv.org/abs/2103.04817","open_access":"1"}],"status":"public","article_processing_charge":"No","department":[{"_id":"LaEr"}],"publication":"arXiv","language":[{"iso":"eng"}],"abstract":[{"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.","lang":"eng"}],"publication_status":"submitted","date_updated":"2025-04-14T07:43:51Z","oa_version":"Preprint","title":"Maxima of a random model of the Riemann zeta function over intervals of varying length","doi":"10.48550/arXiv.2103.04817","author":[{"first_name":"Louis-Pierre","last_name":"Arguin","full_name":"Arguin, Louis-Pierre"},{"full_name":"Dubach, Guillaume","id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E","first_name":"Guillaume","orcid":"0000-0001-6892-8137","last_name":"Dubach"},{"full_name":"Hartung, Lisa","first_name":"Lisa","last_name":"Hartung"}],"date_created":"2021-03-09T11:08:15Z","month":"03","_id":"9230","arxiv":1,"citation":{"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>","short":"L.-P. Arguin, G. Dubach, L. Hartung, ArXiv (n.d.).","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>.","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>","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>. .","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."},"oa":1,"date_published":"2021-03-08T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"08","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.","ec_funded":1,"type":"preprint","project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020"}],"year":"2021"},{"ec_funded":1,"project":[{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"type":"preprint","year":"2021","date_created":"2021-03-23T05:38:48Z","doi":"10.48550/arXiv.2103.11389","author":[{"first_name":"Guillaume","orcid":"0000-0001-6892-8137","last_name":"Dubach","full_name":"Dubach, Guillaume","id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E"},{"full_name":"Mühlböck, Fabian","id":"6395C5F6-89DF-11E9-9C97-6BDFE5697425","first_name":"Fabian","orcid":"0000-0003-1548-0177","last_name":"Mühlböck"}],"month":"03","corr_author":"1","_id":"9281","citation":{"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>. .","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>.","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>.","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>","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>"},"arxiv":1,"date_published":"2021-03-21T00:00:00Z","oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"21","language":[{"iso":"eng"}],"related_material":{"record":[{"status":"public","id":"9946","relation":"other"}]},"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."}],"publication_status":"submitted","date_updated":"2025-04-15T06:26:12Z","oa_version":"Preprint","title":"Formal verification of Zagier's one-sentence proof","article_number":"2103.11389","external_id":{"arxiv":["2103.11389"]},"main_file_link":[{"url":"https://arxiv.org/abs/2103.11389","open_access":"1"}],"status":"public","article_processing_charge":"No","department":[{"_id":"LaEr"},{"_id":"ToHe"}],"publication":"arXiv"},{"external_id":{"arxiv":["1911.05112"],"isi":["000681531500001"]},"status":"public","article_processing_charge":"Yes (in subscription journal)","has_accepted_license":"1","department":[{"_id":"LaEr"}],"isi":1,"publication":"Annales Henri Poincaré ","language":[{"iso":"eng"}],"file":[{"relation":"main_file","file_name":"2021_AnnHenriPoincare_Erdoes.pdf","date_created":"2022-05-12T12:50:27Z","checksum":"8d6bac0e2b0a28539608b0538a8e3b38","file_id":"11365","access_level":"open_access","creator":"dernst","content_type":"application/pdf","file_size":1162454,"date_updated":"2022-05-12T12:50:27Z","success":1}],"date_updated":"2025-04-15T08:04:59Z","ddc":["510"],"publisher":"Springer Nature","month":"12","day":"01","ec_funded":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"type":"journal_article","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","grant_number":"338804"}],"year":"2021","page":"4205–4269","file_date_updated":"2022-05-12T12:50:27Z","quality_controlled":"1","abstract":[{"lang":"eng","text":"In the customary random matrix model for transport in quantum dots with M internal degrees of freedom coupled to a chaotic environment via 𝑁≪𝑀 channels, the density 𝜌 of transmission eigenvalues is computed from a specific invariant ensemble for which explicit formula for the joint probability density of all eigenvalues is available. We revisit this problem in the large N regime allowing for (i) arbitrary ratio 𝜙:=𝑁/𝑀≤1; and (ii) general distributions for the matrix elements of the Hamiltonian of the quantum dot. In the limit 𝜙→0, we recover the formula for the density 𝜌 that Beenakker (Rev Mod Phys 69:731–808, 1997) has derived for a special matrix ensemble. We also prove that the inverse square root singularity of the density at zero and full transmission in Beenakker’s formula persists for any 𝜙<1 but in the borderline case 𝜙=1 an anomalous 𝜆−2/3 singularity arises at zero. To access this level of generality, we develop the theory of global and local laws on the spectral density of a large class of noncommutative rational expressions in large random matrices with i.i.d. entries."}],"publication_status":"published","oa_version":"Published Version","title":"Scattering in quantum dots via noncommutative rational functions","doi":"10.1007/s00023-021-01085-6","author":[{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös","first_name":"László"},{"full_name":"Krüger, Torben H","id":"3020C786-F248-11E8-B48F-1D18A9856A87","first_name":"Torben H","last_name":"Krüger","orcid":"0000-0002-4821-3297"},{"full_name":"Nemish, Yuriy","id":"4D902E6A-F248-11E8-B48F-1D18A9856A87","first_name":"Yuriy","last_name":"Nemish","orcid":"0000-0002-7327-856X"}],"date_created":"2021-08-15T22:01:29Z","scopus_import":"1","_id":"9912","citation":{"mla":"Erdös, László, et al. “Scattering in Quantum Dots via Noncommutative Rational Functions.” <i>Annales Henri Poincaré </i>, vol. 22, Springer Nature, 2021, pp. 4205–4269, doi:<a href=\"https://doi.org/10.1007/s00023-021-01085-6\">10.1007/s00023-021-01085-6</a>.","chicago":"Erdös, László, Torben H Krüger, and Yuriy Nemish. “Scattering in Quantum Dots via Noncommutative Rational Functions.” <i>Annales Henri Poincaré </i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00023-021-01085-6\">https://doi.org/10.1007/s00023-021-01085-6</a>.","short":"L. Erdös, T.H. Krüger, Y. Nemish, Annales Henri Poincaré  22 (2021) 4205–4269.","ama":"Erdös L, Krüger TH, Nemish Y. Scattering in quantum dots via noncommutative rational functions. <i>Annales Henri Poincaré </i>. 2021;22:4205–4269. doi:<a href=\"https://doi.org/10.1007/s00023-021-01085-6\">10.1007/s00023-021-01085-6</a>","apa":"Erdös, L., Krüger, T. H., &#38; Nemish, Y. (2021). Scattering in quantum dots via noncommutative rational functions. <i>Annales Henri Poincaré </i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00023-021-01085-6\">https://doi.org/10.1007/s00023-021-01085-6</a>","ista":"Erdös L, Krüger TH, Nemish Y. 2021. Scattering in quantum dots via noncommutative rational functions. Annales Henri Poincaré . 22, 4205–4269.","ieee":"L. Erdös, T. H. Krüger, and Y. Nemish, “Scattering in quantum dots via noncommutative rational functions,” <i>Annales Henri Poincaré </i>, vol. 22. Springer Nature, pp. 4205–4269, 2021."},"arxiv":1,"date_published":"2021-12-01T00:00:00Z","oa":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","acknowledgement":"The authors are very grateful to Yan Fyodorov for discussions on the physical background and for providing references, and to the anonymous referee for numerous valuable remarks.","intvolume":"        22","article_type":"original","volume":22,"publication_identifier":{"eissn":["1424-0661"],"issn":["1424-0637"]}},{"doi":"10.1214/21-EJP591","date_created":"2021-05-23T22:01:44Z","author":[{"first_name":"Giorgio","orcid":"0000-0002-4901-7992","last_name":"Cipolloni","full_name":"Cipolloni, Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","last_name":"Erdös","orcid":"0000-0001-5366-9603"},{"orcid":"0000-0002-2904-1856","last_name":"Schröder","first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","full_name":"Schröder, Dominik J"}],"_id":"9412","scopus_import":"1","oa":1,"date_published":"2021-03-23T00:00:00Z","arxiv":1,"citation":{"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>","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>.","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>.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Electronic Journal of Probability 26 (2021).","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>","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.","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."},"user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","intvolume":"        26","publication_identifier":{"eissn":["1083-6489"]},"volume":26,"file_date_updated":"2021-05-25T13:24:19Z","quality_controlled":"1","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."}],"publication_status":"published","title":"Fluctuation around the circular law for random matrices with real entries","oa_version":"Published Version","publisher":"Institute of Mathematical Statistics","month":"03","day":"23","ec_funded":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"project":[{"name":"International IST Doctoral Program","call_identifier":"H2020","grant_number":"665385","_id":"2564DBCA-B435-11E9-9278-68D0E5697425"}],"type":"journal_article","year":"2021","external_id":{"arxiv":["2002.02438"],"isi":["000641855600001"]},"article_number":"24","status":"public","article_processing_charge":"No","publication":"Electronic Journal of Probability","has_accepted_license":"1","isi":1,"department":[{"_id":"LaEr"}],"language":[{"iso":"eng"}],"ddc":["510"],"date_updated":"2026-04-02T14:00:37Z","file":[{"success":1,"content_type":"application/pdf","file_size":865148,"date_updated":"2021-05-25T13:24:19Z","creator":"kschuh","access_level":"open_access","checksum":"864ab003ad4cffea783f65aa8c2ba69f","file_name":"2021_EJP_Cipolloni.pdf","file_id":"9423","date_created":"2021-05-25T13:24:19Z","relation":"main_file"}]},{"day":"01","corr_author":"1","month":"02","publisher":"Springer Nature","year":"2021","project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"},{"grant_number":"338804","call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"},{"_id":"2564DBCA-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"International IST Doctoral Program","grant_number":"665385"}],"type":"journal_article","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"ec_funded":1,"publication":"Probability Theory and Related Fields","has_accepted_license":"1","isi":1,"department":[{"_id":"LaEr"}],"article_processing_charge":"Yes (via OA deal)","status":"public","external_id":{"arxiv":["1908.00969"],"isi":["000572724600002"]},"file":[{"success":1,"content_type":"application/pdf","date_updated":"2020-10-05T14:53:40Z","file_size":497032,"relation":"main_file","access_level":"open_access","creator":"dernst","file_name":"2020_ProbTheory_Cipolloni.pdf","date_created":"2020-10-05T14:53:40Z","checksum":"611ae28d6055e1e298d53a57beb05ef4","file_id":"8612"}],"date_updated":"2026-04-02T14:03:52Z","ddc":["510"],"language":[{"iso":"eng"}],"user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","date_published":"2021-02-01T00:00:00Z","oa":1,"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.","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>","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>.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Probability Theory and Related Fields (2021).","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>.","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>"},"arxiv":1,"_id":"8601","scopus_import":"1","doi":"10.1007/s00440-020-01003-7","author":[{"orcid":"0000-0002-4901-7992","last_name":"Cipolloni","first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio"},{"last_name":"Erdös","orcid":"0000-0001-5366-9603","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László"},{"full_name":"Schröder, Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J","last_name":"Schröder","orcid":"0000-0002-2904-1856"}],"date_created":"2020-10-04T22:01:37Z","publication_identifier":{"eissn":["1432-2064"],"issn":["0178-8051"]},"article_type":"original","file_date_updated":"2020-10-05T14:53:40Z","quality_controlled":"1","title":"Edge universality for non-Hermitian random matrices","oa_version":"Published Version","publication_status":"published","abstract":[{"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.","lang":"eng"}]},{"ddc":["510"],"file":[{"success":1,"file_size":483458,"date_updated":"2021-06-15T14:40:45Z","content_type":"application/pdf","creator":"cziletti","access_level":"open_access","date_created":"2021-06-15T14:40:45Z","checksum":"47c986578de132200d41e6d391905519","file_name":"2021_ForumMath_Bao.pdf","file_id":"9555","relation":"main_file"}],"date_updated":"2026-04-07T08:36:39Z","language":[{"iso":"eng"}],"article_processing_charge":"No","isi":1,"has_accepted_license":"1","department":[{"_id":"LaEr"}],"publication":"Forum of Mathematics, Sigma","article_number":"e44","external_id":{"arxiv":["2008.07061"],"isi":["000654960800001"]},"status":"public","type":"journal_article","project":[{"call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"year":"2021","ec_funded":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"day":"27","publisher":"Cambridge University Press","month":"05","publication_status":"published","title":"Equipartition principle for Wigner matrices","oa_version":"Published Version","abstract":[{"lang":"eng","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. "}],"file_date_updated":"2021-06-15T14:40:45Z","quality_controlled":"1","article_type":"original","volume":9,"publication_identifier":{"eissn":["2050-5094"]},"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","intvolume":"         9","arxiv":1,"citation":{"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.","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>","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>.","short":"Z. Bao, L. Erdös, K. Schnelli, Forum of Mathematics, Sigma 9 (2021).","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>.","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>"},"oa":1,"date_published":"2021-05-27T00:00:00Z","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","doi":"10.1017/fms.2021.38","author":[{"id":"442E6A6C-F248-11E8-B48F-1D18A9856A87","full_name":"Bao, Zhigang","orcid":"0000-0003-3036-1475","last_name":"Bao","first_name":"Zhigang"},{"full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","orcid":"0000-0001-5366-9603","last_name":"Erdös"},{"last_name":"Schnelli","orcid":"0000-0003-0954-3231","first_name":"Kevin","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","full_name":"Schnelli, Kevin"}],"date_created":"2021-06-13T22:01:33Z","scopus_import":"1","_id":"9550"}]