[{"oa":1,"oa_version":"Published Version","scopus_import":"1","year":"2022","has_accepted_license":"1","department":[{"_id":"LaEr"}],"license":"https://creativecommons.org/licenses/by/4.0/","acknowledgement":"Open access funding provided by Swiss Federal Institute of Technology Zurich. Supported by Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zürich Foundation.","page":"3981-4002","file_date_updated":"2023-01-27T11:06:47Z","abstract":[{"lang":"eng","text":"We derive a precise asymptotic formula for the density of the small singular values of the real Ginibre matrix ensemble shifted by a complex parameter z as the dimension tends to infinity. For z away from the real axis the formula coincides with that for the complex Ginibre ensemble we derived earlier in Cipolloni et al. (Prob Math Phys 1:101–146, 2020). On the level of the one-point function of the low lying singular values we thus confirm the transition from real to complex Ginibre ensembles as the shift parameter z becomes genuinely complex; the analogous phenomenon has been well known for eigenvalues. We use the superbosonization formula (Littelmann et al. in Comm Math Phys 283:343–395, 2008) in a regime where the main contribution comes from a three dimensional saddle manifold."}],"date_created":"2023-01-16T09:50:26Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"article_type":"original","file":[{"content_type":"application/pdf","file_id":"12424","creator":"dernst","success":1,"access_level":"open_access","checksum":"5582f059feeb2f63e2eb68197a34d7dc","date_created":"2023-01-27T11:06:47Z","file_size":1333638,"date_updated":"2023-01-27T11:06:47Z","relation":"main_file","file_name":"2022_AnnalesHenriP_Cipolloni.pdf"}],"citation":{"ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Density of small singular values of the shifted real Ginibre ensemble,” <i>Annales Henri Poincaré</i>, vol. 23, no. 11. Springer Nature, pp. 3981–4002, 2022.","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2022). Density of small singular values of the shifted real Ginibre ensemble. <i>Annales Henri Poincaré</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00023-022-01188-8\">https://doi.org/10.1007/s00023-022-01188-8</a>","mla":"Cipolloni, Giorgio, et al. “Density of Small Singular Values of the Shifted Real Ginibre Ensemble.” <i>Annales Henri Poincaré</i>, vol. 23, no. 11, Springer Nature, 2022, pp. 3981–4002, doi:<a href=\"https://doi.org/10.1007/s00023-022-01188-8\">10.1007/s00023-022-01188-8</a>.","ama":"Cipolloni G, Erdös L, Schröder DJ. Density of small singular values of the shifted real Ginibre ensemble. <i>Annales Henri Poincaré</i>. 2022;23(11):3981-4002. doi:<a href=\"https://doi.org/10.1007/s00023-022-01188-8\">10.1007/s00023-022-01188-8</a>","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Density of Small Singular Values of the Shifted Real Ginibre Ensemble.” <i>Annales Henri Poincaré</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s00023-022-01188-8\">https://doi.org/10.1007/s00023-022-01188-8</a>.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Annales Henri Poincaré 23 (2022) 3981–4002.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Density of small singular values of the shifted real Ginibre ensemble. Annales Henri Poincaré. 23(11), 3981–4002."},"author":[{"full_name":"Cipolloni, Giorgio","last_name":"Cipolloni","orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio"},{"last_name":"Erdös","full_name":"Erdös, László","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603"},{"last_name":"Schröder","full_name":"Schröder, Dominik J","first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856"}],"title":"Density of small singular values of the shifted real Ginibre ensemble","ddc":["510"],"issue":"11","month":"11","doi":"10.1007/s00023-022-01188-8","_id":"12232","quality_controlled":"1","date_updated":"2023-08-04T09:33:52Z","date_published":"2022-11-01T00:00:00Z","status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","type":"journal_article","article_processing_charge":"No","isi":1,"keyword":["Mathematical Physics","Nuclear and High Energy Physics","Statistical and Nonlinear Physics"],"publisher":"Springer Nature","intvolume":"        23","publication_identifier":{"issn":["1424-0637"],"eissn":["1424-0661"]},"volume":23,"language":[{"iso":"eng"}],"day":"01","external_id":{"isi":["000796323500001"]},"publication":"Annales Henri Poincaré","publication_status":"published"},{"article_type":"original","file":[{"file_name":"2022_JourMathPhysics_Cipolloni2.pdf","file_size":7356807,"access_level":"open_access","checksum":"2db278ae5b07f345a7e3fec1f92b5c33","date_created":"2023-01-30T08:01:10Z","date_updated":"2023-01-30T08:01:10Z","relation":"main_file","creator":"dernst","file_id":"12436","success":1,"content_type":"application/pdf"}],"citation":{"ista":"Cipolloni G, Erdös L, Schröder DJ, Xu Y. 2022. Directional extremal statistics for Ginibre eigenvalues. Journal of Mathematical Physics. 63(10), 103303.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Y. Xu, Journal of Mathematical Physics 63 (2022).","ama":"Cipolloni G, Erdös L, Schröder DJ, Xu Y. Directional extremal statistics for Ginibre eigenvalues. <i>Journal of Mathematical Physics</i>. 2022;63(10). doi:<a href=\"https://doi.org/10.1063/5.0104290\">10.1063/5.0104290</a>","chicago":"Cipolloni, Giorgio, László Erdös, Dominik J Schröder, and Yuanyuan Xu. “Directional Extremal Statistics for Ginibre Eigenvalues.” <i>Journal of Mathematical Physics</i>. AIP Publishing, 2022. <a href=\"https://doi.org/10.1063/5.0104290\">https://doi.org/10.1063/5.0104290</a>.","mla":"Cipolloni, Giorgio, et al. “Directional Extremal Statistics for Ginibre Eigenvalues.” <i>Journal of Mathematical Physics</i>, vol. 63, no. 10, 103303, AIP Publishing, 2022, doi:<a href=\"https://doi.org/10.1063/5.0104290\">10.1063/5.0104290</a>.","apa":"Cipolloni, G., Erdös, L., Schröder, D. J., &#38; Xu, Y. (2022). Directional extremal statistics for Ginibre eigenvalues. <i>Journal of Mathematical Physics</i>. AIP Publishing. <a href=\"https://doi.org/10.1063/5.0104290\">https://doi.org/10.1063/5.0104290</a>","ieee":"G. Cipolloni, L. Erdös, D. J. Schröder, and Y. Xu, “Directional extremal statistics for Ginibre eigenvalues,” <i>Journal of Mathematical Physics</i>, vol. 63, no. 10. AIP Publishing, 2022."},"author":[{"full_name":"Cipolloni, Giorgio","last_name":"Cipolloni","orcid":"0000-0002-4901-7992","first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Erdös","full_name":"Erdös, László","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603"},{"full_name":"Schröder, Dominik J","last_name":"Schröder","orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J"},{"id":"7902bdb1-a2a4-11eb-a164-c9216f71aea3","first_name":"Yuanyuan","orcid":"0000-0003-1559-1205","last_name":"Xu","full_name":"Xu, Yuanyuan"}],"title":"Directional extremal statistics for Ginibre eigenvalues","department":[{"_id":"LaEr"}],"acknowledgement":"The authors are grateful to G. Akemann for bringing Refs. 19 and 24–26 to their attention. Discussions with Guillaume Dubach on a preliminary version of this project are acknowledged.\r\nL.E. and Y.X. were supported by the ERC Advanced Grant “RMTBeyond” under Grant No. 101020331. D.S. was supported by Dr. Max Rössler, the Walter Haefner Foundation, and the ETH Zürich Foundation.","abstract":[{"text":"We consider the eigenvalues of a large dimensional real or complex Ginibre matrix in the region of the complex plane where their real parts reach their maximum value. This maximum follows the Gumbel distribution and that these extreme eigenvalues form a Poisson point process as the dimension asymptotically tends to infinity. In the complex case, these facts have already been established by Bender [Probab. Theory Relat. Fields 147, 241 (2010)] and in the real case by Akemann and Phillips [J. Stat. Phys. 155, 421 (2014)] even for the more general elliptic ensemble with a sophisticated saddle point analysis. The purpose of this article is to give a very short direct proof in the Ginibre case with an effective error term. Moreover, our estimates on the correlation kernel in this regime serve as a key input for accurately locating [Formula: see text] for any large matrix X with i.i.d. entries in the companion paper [G. Cipolloni et al., arXiv:2206.04448 (2022)]. ","lang":"eng"}],"file_date_updated":"2023-01-30T08:01:10Z","date_created":"2023-01-16T09:52:58Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"year":"2022","article_number":"103303","has_accepted_license":"1","oa":1,"oa_version":"Published Version","scopus_import":"1","language":[{"iso":"eng"}],"day":"14","external_id":{"arxiv":["2206.04443"],"isi":["000869715800001"]},"publication":"Journal of Mathematical Physics","publication_status":"published","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"isi":1,"ec_funded":1,"intvolume":"        63","publisher":"AIP Publishing","publication_identifier":{"issn":["0022-2488"],"eissn":["1089-7658"]},"volume":63,"project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"date_published":"2022-10-14T00:00:00Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","type":"journal_article","article_processing_charge":"Yes (via OA deal)","ddc":["510","530"],"issue":"10","arxiv":1,"month":"10","doi":"10.1063/5.0104290","_id":"12243","date_updated":"2025-04-14T07:57:18Z","quality_controlled":"1"},{"article_processing_charge":"No","date_published":"2022-09-12T00:00:00Z","status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","type":"journal_article","_id":"12290","quality_controlled":"1","date_updated":"2025-04-14T07:57:19Z","ddc":["510"],"doi":"10.1214/22-ejp838","month":"09","publication":"Electronic Journal of Probability","external_id":{"isi":["000910863700003"]},"corr_author":"1","publication_status":"published","language":[{"iso":"eng"}],"day":"12","publication_identifier":{"eissn":["1083-6489"]},"volume":27,"project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"isi":1,"keyword":["Statistics","Probability and Uncertainty","Statistics and Probability"],"ec_funded":1,"publisher":"Institute of Mathematical Statistics","intvolume":"        27","has_accepted_license":"1","year":"2022","oa_version":"Published Version","scopus_import":"1","oa":1,"author":[{"orcid":"0000-0002-4901-7992","first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio","last_name":"Cipolloni"},{"orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","full_name":"Erdös, László","last_name":"Erdös"},{"full_name":"Schröder, Dominik J","last_name":"Schröder","orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J"}],"citation":{"apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2022). Optimal multi-resolvent local laws for Wigner matrices. <i>Electronic Journal of Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/22-ejp838\">https://doi.org/10.1214/22-ejp838</a>","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Optimal multi-resolvent local laws for Wigner matrices,” <i>Electronic Journal of Probability</i>, vol. 27. Institute of Mathematical Statistics, pp. 1–38, 2022.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Electronic Journal of Probability 27 (2022) 1–38.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Optimal multi-resolvent local laws for Wigner matrices. Electronic Journal of Probability. 27, 1–38.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Optimal Multi-Resolvent Local Laws for Wigner Matrices.” <i>Electronic Journal of Probability</i>. Institute of Mathematical Statistics, 2022. <a href=\"https://doi.org/10.1214/22-ejp838\">https://doi.org/10.1214/22-ejp838</a>.","ama":"Cipolloni G, Erdös L, Schröder DJ. Optimal multi-resolvent local laws for Wigner matrices. <i>Electronic Journal of Probability</i>. 2022;27:1-38. doi:<a href=\"https://doi.org/10.1214/22-ejp838\">10.1214/22-ejp838</a>","mla":"Cipolloni, Giorgio, et al. “Optimal Multi-Resolvent Local Laws for Wigner Matrices.” <i>Electronic Journal of Probability</i>, vol. 27, Institute of Mathematical Statistics, 2022, pp. 1–38, doi:<a href=\"https://doi.org/10.1214/22-ejp838\">10.1214/22-ejp838</a>."},"title":"Optimal multi-resolvent local laws for Wigner matrices","article_type":"original","file":[{"date_updated":"2023-01-30T11:59:21Z","relation":"main_file","file_size":502149,"access_level":"open_access","date_created":"2023-01-30T11:59:21Z","checksum":"bb647b48fbdb59361210e425c220cdcb","file_name":"2022_ElecJournProbability_Cipolloni.pdf","content_type":"application/pdf","success":1,"creator":"dernst","file_id":"12464"}],"abstract":[{"lang":"eng","text":"We prove local laws, i.e. optimal concentration estimates for arbitrary products of resolvents of a Wigner random matrix with deterministic matrices in between. We find that the size of such products heavily depends on whether some of the deterministic matrices are traceless. Our estimates correctly account for this dependence and they hold optimally down to the smallest possible spectral scale."}],"file_date_updated":"2023-01-30T11:59:21Z","date_created":"2023-01-16T10:04:38Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"department":[{"_id":"LaEr"}],"acknowledgement":"L. Erdős was supported by ERC Advanced Grant “RMTBeyond” No. 101020331. D. Schröder was supported by Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zürich Foundation.","page":"1-38"},{"month":"01","doi":"10.1063/5.0051632","issue":"1","arxiv":1,"_id":"10600","date_updated":"2025-04-14T07:57:17Z","quality_controlled":"1","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2012.15238","open_access":"1"}],"status":"public","type":"journal_article","date_published":"2022-01-03T00:00:00Z","article_processing_charge":"No","ec_funded":1,"publisher":"AIP Publishing","intvolume":"        63","isi":1,"keyword":["mathematical physics","statistical and nonlinear physics"],"publication_identifier":{"eissn":["1089-7658"],"issn":["0022-2488"]},"volume":63,"project":[{"call_identifier":"H2020","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"day":"03","language":[{"iso":"eng"}],"publication_status":"published","external_id":{"isi":["000739446000009"],"arxiv":["2012.15238"]},"publication":"Journal of Mathematical Physics","oa":1,"scopus_import":"1","oa_version":"Preprint","article_number":"011901","year":"2022","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"acknowledgement":"J.H. acknowledges partial financial support from ERC Advanced Grant “RMTBeyond” No. 101020331.","abstract":[{"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.","lang":"eng"}],"date_created":"2022-01-03T12:19:48Z","article_type":"original","title":"Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap","author":[{"full_name":"Henheik, Sven Joscha","last_name":"Henheik","orcid":"0000-0003-1106-327X","first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb"},{"last_name":"Teufel","full_name":"Teufel, Stefan","first_name":"Stefan"}],"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.","short":"S.J. Henheik, S. Teufel, Journal of Mathematical Physics 63 (2022).","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>","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>.","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."}},{"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","type":"journal_article","date_published":"2022-01-18T00:00:00Z","article_processing_charge":"Yes","month":"01","doi":"10.1017/fms.2021.80","ddc":["510"],"arxiv":1,"_id":"10643","date_updated":"2025-04-14T07:57:17Z","quality_controlled":"1","day":"18","language":[{"iso":"eng"}],"publication_status":"published","publication":"Forum of Mathematics, Sigma","external_id":{"arxiv":["2012.15239"],"isi":["000743615000001"]},"corr_author":"1","intvolume":"        10","publisher":"Cambridge University Press","ec_funded":1,"isi":1,"keyword":["computational mathematics","discrete mathematics and combinatorics","geometry and topology","mathematical physics","statistics and probability","algebra and number theory","theoretical computer science","analysis"],"volume":10,"publication_identifier":{"eissn":["2050-5094"]},"project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"article_number":"e4","year":"2022","has_accepted_license":"1","oa":1,"scopus_import":"1","oa_version":"Published Version","article_type":"original","file":[{"file_name":"2022_ForumMathSigma_Henheik.pdf","date_updated":"2022-01-19T09:27:43Z","relation":"main_file","file_size":705323,"date_created":"2022-01-19T09:27:43Z","checksum":"87592a755adcef22ea590a99dc728dd3","access_level":"open_access","success":1,"creator":"cchlebak","file_id":"10646","content_type":"application/pdf"}],"title":"Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk","author":[{"orcid":"0000-0003-1106-327X","first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","full_name":"Henheik, Sven Joscha","last_name":"Henheik"},{"first_name":"Stefan","full_name":"Teufel, Stefan","last_name":"Teufel"}],"citation":{"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>.","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>","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>.","short":"S.J. Henheik, S. Teufel, Forum of Mathematics, Sigma 10 (2022).","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>"},"department":[{"_id":"GradSch"},{"_id":"LaEr"}],"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.","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"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"}],"file_date_updated":"2022-01-19T09:27:43Z","date_created":"2022-01-18T16:18:51Z"},{"department":[{"_id":"LaEr"}],"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.","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"}],"file_date_updated":"2022-07-29T07:22:08Z","date_created":"2022-02-06T23:01:30Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"article_type":"original","file":[{"date_updated":"2022-07-29T07:22:08Z","relation":"main_file","file_size":652573,"access_level":"open_access","date_created":"2022-07-29T07:22:08Z","checksum":"b75fdad606ab507dc61109e0907d86c0","file_name":"2022_JourFunctionalAnalysis_Cipolloni.pdf","content_type":"application/pdf","success":1,"creator":"dernst","file_id":"11690"}],"author":[{"last_name":"Cipolloni","full_name":"Cipolloni, Giorgio","first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992"},{"last_name":"Erdös","full_name":"Erdös, László","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603"},{"full_name":"Schröder, Dominik J","last_name":"Schröder","orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J"}],"citation":{"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>","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>.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Thermalisation for Wigner matrices. Journal of Functional Analysis. 282(8), 109394.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Journal of Functional Analysis 282 (2022).","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>"},"title":"Thermalisation for Wigner matrices","oa":1,"oa_version":"Published Version","scopus_import":"1","year":"2022","article_number":"109394","has_accepted_license":"1","isi":1,"intvolume":"       282","publisher":"Elsevier","publication_identifier":{"eissn":["1096-0783"],"issn":["0022-1236"]},"volume":282,"language":[{"iso":"eng"}],"day":"15","external_id":{"arxiv":["2102.09975"],"isi":["000781239100004"]},"publication":"Journal of Functional Analysis","corr_author":"1","publication_status":"published","issue":"8","ddc":["500"],"arxiv":1,"month":"04","doi":"10.1016/j.jfa.2022.109394","_id":"10732","quality_controlled":"1","date_updated":"2024-10-09T21:01:33Z","date_published":"2022-04-15T00:00:00Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","type":"journal_article","article_processing_charge":"Yes (via OA deal)"},{"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.","department":[{"_id":"LaEr"}],"page":"839-907","date_created":"2022-04-24T22:01:44Z","abstract":[{"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.","lang":"eng"}],"file_date_updated":"2022-08-05T06:01:13Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"file":[{"relation":"main_file","date_updated":"2022-08-05T06:01:13Z","access_level":"open_access","date_created":"2022-08-05T06:01:13Z","checksum":"bee0278c5efa9a33d9a2dc8d354a6c51","file_size":1141462,"file_name":"2022_CommunMathPhys_Schnelli.pdf","content_type":"application/pdf","success":1,"creator":"dernst","file_id":"11726"}],"article_type":"original","pmid":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.","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>.","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>","short":"K. Schnelli, Y. Xu, Communications in Mathematical Physics 393 (2022) 839–907.","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."},"author":[{"last_name":"Schnelli","full_name":"Schnelli, Kevin","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","first_name":"Kevin","orcid":"0000-0003-0954-3231"},{"last_name":"Xu","full_name":"Xu, Yuanyuan","first_name":"Yuanyuan","id":"7902bdb1-a2a4-11eb-a164-c9216f71aea3","orcid":"0000-0003-1559-1205"}],"title":"Convergence rate to the Tracy–Widom laws for the largest Eigenvalue of Wigner matrices","oa":1,"oa_version":"Published Version","scopus_import":"1","year":"2022","has_accepted_license":"1","isi":1,"intvolume":"       393","publisher":"Springer Nature","ec_funded":1,"project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"volume":393,"publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"language":[{"iso":"eng"}],"day":"01","external_id":{"arxiv":["2102.04330"],"isi":["000782737200001"],"pmid":["35765414"]},"publication":"Communications in Mathematical Physics","publication_status":"published","arxiv":1,"ddc":["510"],"month":"07","doi":"10.1007/s00220-022-04377-y","quality_controlled":"1","date_updated":"2025-06-11T14:01:05Z","_id":"11332","date_published":"2022-07-01T00:00:00Z","type":"journal_article","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No"},{"day":"01","language":[{"iso":"eng"}],"publication_status":"published","external_id":{"isi":["000793963400005"],"arxiv":["2103.06730"]},"publication":"Annals of Probability","publisher":"Institute of Mathematical Statistics","intvolume":"        50","isi":1,"publication_identifier":{"eissn":["2168-894X"],"issn":["0091-1798"]},"volume":50,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2103.06730"}],"type":"journal_article","date_published":"2022-05-01T00:00:00Z","article_processing_charge":"No","doi":"10.1214/21-AOP1552","month":"05","issue":"3","arxiv":1,"_id":"11418","quality_controlled":"1","date_updated":"2023-08-03T07:16:53Z","article_type":"original","title":"Normal fluctuation in quantum ergodicity for Wigner matrices","author":[{"orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio","full_name":"Cipolloni, Giorgio","last_name":"Cipolloni"},{"orcid":"0000-0001-5366-9603","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","last_name":"Erdös"},{"full_name":"Schröder, Dominik J","last_name":"Schröder","orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J"}],"citation":{"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>","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.","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>","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>.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Annals of Probability 50 (2022) 984–1012.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Normal fluctuation in quantum ergodicity for Wigner matrices. Annals of Probability. 50(3), 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>."},"page":"984-1012","department":[{"_id":"LaEr"}],"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.","abstract":[{"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).","lang":"eng"}],"date_created":"2022-05-29T22:01:53Z","year":"2022","oa":1,"scopus_import":"1","oa_version":"Preprint"},{"file":[{"creator":"cchlebak","file_id":"10624","success":1,"content_type":"application/pdf","file_name":"2022_MathPhyAnalGeo_Henheik.pdf","access_level":"open_access","date_created":"2022-01-14T07:27:45Z","checksum":"d44f8123a52592a75b2c3b8ee2cd2435","file_size":505804,"relation":"main_file","date_updated":"2022-01-14T07:27:45Z"}],"article_type":"original","author":[{"orcid":"0000-0003-1106-327X","first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","full_name":"Henheik, Sven Joscha","last_name":"Henheik"}],"citation":{"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.","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>","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>.","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>","ista":"Henheik SJ. 2022. The BCS critical temperature at high density. Mathematical Physics, Analysis and Geometry. 25(1), 3.","short":"S.J. Henheik, Mathematical Physics, Analysis and Geometry 25 (2022)."},"title":"The BCS critical temperature at high density","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.","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"date_created":"2022-01-13T15:40:53Z","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"}],"file_date_updated":"2022-01-14T07:27:45Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"year":"2022","article_number":"3","has_accepted_license":"1","oa":1,"oa_version":"Published Version","scopus_import":"1","language":[{"iso":"eng"}],"day":"11","corr_author":"1","publication":"Mathematical Physics, Analysis and Geometry","external_id":{"isi":["000741387600001"],"arxiv":["2106.02015"]},"publication_status":"published","keyword":["geometry and topology","mathematical physics"],"isi":1,"publisher":"Springer Nature","intvolume":"        25","ec_funded":1,"project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"publication_identifier":{"eissn":["1572-9656"],"issn":["1385-0172"]},"volume":25,"related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"19540"}]},"date_published":"2022-01-11T00:00:00Z","type":"journal_article","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","article_processing_charge":"Yes (via OA deal)","arxiv":1,"ddc":["514"],"issue":"1","doi":"10.1007/s11040-021-09415-0","month":"01","date_updated":"2026-04-07T12:37:10Z","quality_controlled":"1","_id":"10623"},{"scopus_import":"1","oa_version":"Published Version","oa":1,"has_accepted_license":"1","article_number":"121101","year":"2022","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"file_date_updated":"2023-01-27T07:10:52Z","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_created":"2023-01-15T23:00:52Z","department":[{"_id":"LaEr"}],"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.\" ","title":"On adiabatic theory for extended fermionic lattice systems","author":[{"full_name":"Henheik, Sven Joscha","last_name":"Henheik","orcid":"0000-0003-1106-327X","first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb"},{"first_name":"Tom","last_name":"Wessel","full_name":"Wessel, Tom"}],"citation":{"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>.","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).","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.","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>"},"article_type":"original","file":[{"date_updated":"2023-01-27T07:10:52Z","relation":"main_file","file_size":5251092,"date_created":"2023-01-27T07:10:52Z","checksum":"213b93750080460718c050e4967cfdb4","access_level":"open_access","file_name":"2022_JourMathPhysics_Henheik2.pdf","content_type":"application/pdf","success":1,"file_id":"12410","creator":"dernst"}],"_id":"12184","date_updated":"2026-04-07T12:37:10Z","quality_controlled":"1","doi":"10.1063/5.0123441","month":"12","ddc":["510"],"issue":"12","arxiv":1,"article_processing_charge":"No","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","type":"journal_article","date_published":"2022-12-01T00:00:00Z","related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"19540"}]},"volume":63,"publication_identifier":{"issn":["0022-2488"]},"project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"publisher":"AIP Publishing","ec_funded":1,"intvolume":"        63","isi":1,"publication_status":"published","external_id":{"arxiv":["2208.12220"],"isi":["000905776200001"]},"publication":"Journal of Mathematical Physics","corr_author":"1","day":"01","language":[{"iso":"eng"}]},{"oa":1,"scopus_import":"1","oa_version":"Published Version","article_number":"9","year":"2022","has_accepted_license":"1","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"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":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"file_date_updated":"2022-01-19T09:41:14Z","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."}],"date_created":"2022-01-18T16:18:25Z","pmid":1,"article_type":"original","file":[{"file_name":"2022_LettersMathPhys_Henheik.pdf","file_size":357547,"date_created":"2022-01-19T09:41:14Z","access_level":"open_access","checksum":"7e8e69b76e892c305071a4736131fe18","date_updated":"2022-01-19T09:41:14Z","relation":"main_file","file_id":"10647","creator":"cchlebak","success":1,"content_type":"application/pdf"}],"title":"Local stability of ground states in locally gapped and weakly interacting quantum spin systems","citation":{"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>.","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>","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.","short":"S.J. Henheik, S. Teufel, T. Wessel, Letters in Mathematical Physics 112 (2022).","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>"},"author":[{"orcid":"0000-0003-1106-327X","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha","full_name":"Henheik, Sven Joscha","last_name":"Henheik"},{"first_name":"Stefan","last_name":"Teufel","full_name":"Teufel, Stefan"},{"first_name":"Tom","full_name":"Wessel, Tom","last_name":"Wessel"}],"doi":"10.1007/s11005-021-01494-y","month":"01","issue":"1","ddc":["530"],"arxiv":1,"_id":"10642","quality_controlled":"1","date_updated":"2026-04-07T12:37:10Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","type":"journal_article","date_published":"2022-01-18T00:00:00Z","article_processing_charge":"No","publisher":"Springer Nature","intvolume":"       112","ec_funded":1,"keyword":["mathematical physics","statistical and nonlinear physics"],"isi":1,"related_material":{"record":[{"status":"public","id":"19540","relation":"dissertation_contains"}]},"volume":112,"publication_identifier":{"issn":["0377-9017"],"eissn":["1573-0530"]},"project":[{"call_identifier":"H2020","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"day":"18","language":[{"iso":"eng"}],"publication_status":"published","external_id":{"pmid":["35125630"],"isi":["000744930400001"],"arxiv":["2106.13780"]},"publication":"Letters in Mathematical Physics"},{"month":"07","doi":"10.1007/s10955-022-02965-9","ddc":["530"],"quality_controlled":"1","date_updated":"2026-04-07T13:01:40Z","_id":"11732","type":"journal_article","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","status":"public","date_published":"2022-07-29T00:00:00Z","article_processing_charge":"Yes (via OA deal)","publisher":"Springer Nature","ec_funded":1,"intvolume":"       189","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"isi":1,"related_material":{"record":[{"id":"19540","status":"public","relation":"dissertation_contains"},{"id":"18135","status":"public","relation":"dissertation_contains"}]},"project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"volume":189,"publication_identifier":{"eissn":["1572-9613"],"issn":["0022-4715"]},"day":"29","language":[{"iso":"eng"}],"publication_status":"published","corr_author":"1","publication":"Journal of Statistical Physics","external_id":{"isi":["000833007200002"]},"oa":1,"scopus_import":"1","oa_version":"Published Version","article_number":"5","year":"2022","has_accepted_license":"1","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)","department":[{"_id":"GradSch"},{"_id":"LaEr"},{"_id":"RoSe"}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"date_created":"2022-08-05T11:36:56Z","abstract":[{"lang":"eng","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."}],"file_date_updated":"2022-08-08T07:36:34Z","file":[{"content_type":"application/pdf","creator":"dernst","file_id":"11746","success":1,"checksum":"b398c4dbf65f71d417981d6e366427e9","access_level":"open_access","date_created":"2022-08-08T07:36:34Z","file_size":419563,"date_updated":"2022-08-08T07:36:34Z","relation":"main_file","file_name":"2022_JourStatisticalPhysics_Henheik.pdf"}],"article_type":"original","title":"The BCS energy gap at high density","citation":{"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.","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>.","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>","short":"S.J. Henheik, A.B. Lauritsen, Journal of Statistical Physics 189 (2022).","ista":"Henheik SJ, Lauritsen AB. 2022. The BCS energy gap at high density. Journal of Statistical Physics. 189, 5.","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>."},"author":[{"full_name":"Henheik, Sven Joscha","last_name":"Henheik","orcid":"0000-0003-1106-327X","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha"},{"last_name":"Lauritsen","full_name":"Lauritsen, Asbjørn Bækgaard","first_name":"Asbjørn Bækgaard","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1","orcid":"0000-0003-4476-2288"}]},{"oa_version":"Preprint","scopus_import":"1","oa":1,"year":"2022","article_number":"2250036","date_created":"2022-04-08T07:11:12Z","abstract":[{"lang":"eng","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."}],"department":[{"_id":"GradSch"},{"_id":"LaEr"}],"author":[{"full_name":"Reker, Jana","last_name":"Reker","id":"e796e4f9-dc8d-11ea-abe3-97e26a0323e9","first_name":"Jana"}],"citation":{"short":"J. Reker, Random Matrices: Theory and Applications 11 (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.","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>","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>.","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>.","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>","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."},"title":"On the operator norm of a Hermitian random matrix with correlated entries","article_type":"original","date_updated":"2026-04-07T13:02:12Z","quality_controlled":"1","_id":"11135","arxiv":1,"issue":"4","doi":"10.1142/s2010326322500368","month":"10","article_processing_charge":"No","date_published":"2022-10-01T00:00:00Z","type":"journal_article","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","main_file_link":[{"url":" https://doi.org/10.48550/arXiv.2103.03906","open_access":"1"}],"publication_identifier":{"issn":["2010-3263"],"eissn":["2010-3271"]},"volume":11,"related_material":{"record":[{"status":"public","id":"17164","relation":"dissertation_contains"}]},"keyword":["Discrete Mathematics and Combinatorics","Statistics","Probability and Uncertainty","Statistics and Probability","Algebra and Number Theory"],"isi":1,"publisher":"World Scientific Publishing","intvolume":"        11","corr_author":"1","publication":"Random Matrices: Theory and Applications","external_id":{"isi":["000848873800001"],"arxiv":["2103.03906"]},"publication_status":"published","language":[{"iso":"eng"}],"day":"01"},{"article_type":"original","author":[{"last_name":"Alt","full_name":"Alt, Johannes","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87","first_name":"Johannes"},{"last_name":"Erdös","full_name":"Erdös, László","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603"},{"orcid":"0000-0002-4821-3297","id":"3020C786-F248-11E8-B48F-1D18A9856A87","first_name":"Torben H","full_name":"Krüger, Torben H","last_name":"Krüger"}],"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.","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>.","ista":"Alt J, Erdös L, Krüger TH. 2021. Spectral radius of random matrices with independent entries. Probability and Mathematical Physics. 2(2), 221–280.","short":"J. Alt, L. Erdös, T.H. Krüger, Probability and Mathematical Physics 2 (2021) 221–280.","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>.","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>"},"title":"Spectral radius of random matrices with independent entries","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.","department":[{"_id":"LaEr"}],"page":"221-280","date_created":"2024-02-18T23:01:03Z","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."}],"year":"2021","oa":1,"oa_version":"Preprint","scopus_import":"1","language":[{"iso":"eng"}],"day":"21","corr_author":"1","external_id":{"arxiv":["1907.13631"]},"publication":"Probability and Mathematical Physics","publication_status":"published","ec_funded":1,"intvolume":"         2","publisher":"Mathematical Sciences Publishers","project":[{"call_identifier":"FP7","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"volume":2,"publication_identifier":{"eissn":["2690-1005"],"issn":["2690-0998"]},"date_published":"2021-05-21T00:00:00Z","type":"journal_article","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1907.13631"}],"status":"public","article_processing_charge":"No","arxiv":1,"issue":"2","month":"05","doi":"10.2140/pmp.2021.2.221","date_updated":"2025-04-15T08:05:02Z","quality_controlled":"1","_id":"15013"},{"article_processing_charge":"No","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1904.04312"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","status":"public","type":"journal_article","date_published":"2021-07-01T00:00:00Z","_id":"15259","date_updated":"2025-09-10T10:13:20Z","quality_controlled":"1","month":"07","doi":"10.1214/20-aop1496","issue":"4","arxiv":1,"publication_status":"published","publication":"The Annals of Probability","external_id":{"isi":["000681349000008"],"arxiv":["1904.04312"]},"corr_author":"1","day":"01","language":[{"iso":"eng"}],"publication_identifier":{"issn":["0091-1798"]},"volume":49,"project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","grant_number":"754411"}],"intvolume":"        49","ec_funded":1,"publisher":"Institute of Mathematical Statistics","isi":1,"keyword":["Statistics","Probability and Uncertainty","Statistics and Probability"],"year":"2021","scopus_import":"1","oa_version":"Preprint","oa":1,"title":"On words of non-Hermitian random matrices","author":[{"last_name":"Dubach","full_name":"Dubach, Guillaume","first_name":"Guillaume","id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E","orcid":"0000-0001-6892-8137"},{"first_name":"Yuval","last_name":"Peled","full_name":"Peled, Yuval"}],"citation":{"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>","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.","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>.","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.","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>."},"article_type":"original","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."}],"date_created":"2024-04-03T07:19:42Z","page":"1886-1916","department":[{"_id":"LaEr"}],"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."},{"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","type":"journal_article","date_published":"2021-10-29T00:00:00Z","article_processing_charge":"Yes (via OA deal)","month":"10","doi":"10.1007/s00220-021-04239-z","issue":"2","ddc":["510"],"arxiv":1,"_id":"10221","date_updated":"2025-04-15T06:53:08Z","quality_controlled":"1","day":"29","language":[{"iso":"eng"}],"publication_status":"published","external_id":{"isi":["000712232700001"],"arxiv":["2012.13215"]},"publication":"Communications in Mathematical Physics","corr_author":"1","publisher":"Springer Nature","intvolume":"       388","isi":1,"publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"volume":388,"project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"year":"2021","has_accepted_license":"1","oa":1,"scopus_import":"1","oa_version":"Published Version","article_type":"original","file":[{"success":1,"file_id":"10715","creator":"cchlebak","content_type":"application/pdf","file_name":"2021_CommunMathPhys_Cipolloni.pdf","relation":"main_file","date_updated":"2022-02-02T10:19:55Z","file_size":841426,"checksum":"a2c7b6f5d23b5453cd70d1261272283b","date_created":"2022-02-02T10:19:55Z","access_level":"open_access"}],"title":"Eigenstate thermalization hypothesis for Wigner matrices","citation":{"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>.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Communications in Mathematical Physics 388 (2021) 1005–1048.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2021. Eigenstate thermalization hypothesis for Wigner matrices. Communications in Mathematical Physics. 388(2), 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>","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>.","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.","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>"},"author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio","orcid":"0000-0002-4901-7992","last_name":"Cipolloni","full_name":"Cipolloni, Giorgio"},{"full_name":"Erdös, László","last_name":"Erdös","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László"},{"full_name":"Schröder, Dominik J","last_name":"Schröder","orcid":"0000-0002-2904-1856","first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87"}],"page":"1005–1048","department":[{"_id":"LaEr"}],"acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria).","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"file_date_updated":"2022-02-02T10:19:55Z","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"}],"date_created":"2021-11-07T23:01:25Z"},{"oa":1,"scopus_import":"1","oa_version":"Published Version","article_number":"124","year":"2021","has_accepted_license":"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.","department":[{"_id":"LaEr"}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"date_created":"2021-11-14T23:01:25Z","abstract":[{"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.","lang":"eng"}],"file_date_updated":"2021-11-15T10:10:17Z","file":[{"relation":"main_file","date_updated":"2021-11-15T10:10:17Z","date_created":"2021-11-15T10:10:17Z","checksum":"1c975afb31460277ce4d22b93538e5f9","access_level":"open_access","file_size":735940,"file_name":"2021_ElecJournalProb_Dubach.pdf","content_type":"application/pdf","success":1,"file_id":"10288","creator":"cchlebak"}],"article_type":"original","title":"On eigenvector statistics in the spherical and truncated unitary ensembles","author":[{"id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E","first_name":"Guillaume","orcid":"0000-0001-6892-8137","last_name":"Dubach","full_name":"Dubach, Guillaume"}],"citation":{"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>","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.","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>","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>.","short":"G. Dubach, Electronic Journal of Probability 26 (2021).","ista":"Dubach G. 2021. On eigenvector statistics in the spherical and truncated unitary ensembles. Electronic Journal of Probability. 26, 124.","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>."},"doi":"10.1214/21-EJP686","month":"09","ddc":["519"],"quality_controlled":"1","date_updated":"2025-04-14T07:43:47Z","_id":"10285","type":"journal_article","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","status":"public","date_published":"2021-09-28T00:00:00Z","article_processing_charge":"No","publisher":"Institute of Mathematical Statistics","ec_funded":1,"intvolume":"        26","project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","grant_number":"754411"}],"volume":26,"publication_identifier":{"eissn":["1083-6489"]},"day":"28","language":[{"iso":"eng"}],"publication_status":"published","publication":"Electronic Journal of Probability"},{"project":[{"name":"Geometric study of Wasserstein spaces and free probability","call_identifier":"H2020","grant_number":"846294","_id":"26A455A6-B435-11E9-9278-68D0E5697425"},{"name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7","grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"volume":609,"publication_identifier":{"issn":["0024-3795"]},"isi":1,"keyword":["Kubo-Ando mean","weighted multivariate mean","barycenter"],"ec_funded":1,"publisher":"Elsevier","intvolume":"       609","publication":"Linear Algebra and its Applications","external_id":{"arxiv":["2002.11678"],"isi":["000581730500011"]},"publication_status":"published","language":[{"iso":"eng"}],"day":"15","date_updated":"2025-04-14T07:50:40Z","quality_controlled":"1","_id":"8373","arxiv":1,"month":"01","doi":"10.1016/j.laa.2020.09.007","article_processing_charge":"No","date_published":"2021-01-15T00:00:00Z","type":"journal_article","main_file_link":[{"url":"https://arxiv.org/abs/2002.11678","open_access":"1"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","date_created":"2020-09-11T08:35:50Z","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."}],"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.","department":[{"_id":"LaEr"}],"page":"203-217","author":[{"last_name":"Pitrik","full_name":"Pitrik, József","first_name":"József"},{"orcid":"0000-0003-1109-5511","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","first_name":"Daniel","full_name":"Virosztek, Daniel","last_name":"Virosztek"}],"citation":{"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>.","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.","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>","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>"},"title":"A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means","article_type":"original","oa_version":"Preprint","scopus_import":"1","oa":1,"year":"2021"},{"_id":"9036","date_updated":"2025-04-14T07:50:40Z","quality_controlled":"1","doi":"10.1016/j.aim.2021.107595","month":"03","issue":"3","arxiv":1,"article_processing_charge":"No","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","main_file_link":[{"url":"https://arxiv.org/abs/1910.10447","open_access":"1"}],"status":"public","type":"journal_article","date_published":"2021-03-26T00:00:00Z","publication_identifier":{"issn":["0001-8708"]},"volume":380,"project":[{"grant_number":"846294","call_identifier":"H2020","name":"Geometric study of Wasserstein spaces and free probability","_id":"26A455A6-B435-11E9-9278-68D0E5697425"}],"publisher":"Elsevier","intvolume":"       380","ec_funded":1,"keyword":["General Mathematics"],"isi":1,"publication_status":"published","external_id":{"arxiv":["1910.10447"],"isi":["000619676100035"]},"publication":"Advances in Mathematics","day":"26","language":[{"iso":"eng"}],"scopus_import":"1","oa_version":"Preprint","oa":1,"article_number":"107595","year":"2021","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."}],"date_created":"2021-01-22T17:55:17Z","department":[{"_id":"LaEr"}],"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.","title":"The metric property of the quantum Jensen-Shannon divergence","citation":{"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>.","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>.","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>","short":"D. Virosztek, Advances in Mathematics 380 (2021).","ista":"Virosztek D. 2021. The metric property of the quantum Jensen-Shannon divergence. Advances in Mathematics. 380(3), 107595.","ieee":"D. Virosztek, “The metric property of the quantum Jensen-Shannon divergence,” <i>Advances in Mathematics</i>, vol. 380, no. 3. Elsevier, 2021.","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>"},"author":[{"last_name":"Virosztek","full_name":"Virosztek, Daniel","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","first_name":"Daniel","orcid":"0000-0003-1109-5511"}],"article_type":"original"},{"date_updated":"2025-04-14T07:43:51Z","_id":"9230","oa_version":"Preprint","doi":"10.48550/arXiv.2103.04817","month":"03","oa":1,"arxiv":1,"article_processing_charge":"No","type":"preprint","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","main_file_link":[{"url":"https://arxiv.org/abs/2103.04817","open_access":"1"}],"status":"public","article_number":"2103.04817","year":"2021","date_published":"2021-03-08T00:00:00Z","date_created":"2021-03-09T11:08:15Z","project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships"}],"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."}],"ec_funded":1,"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.","department":[{"_id":"LaEr"}],"publication_status":"submitted","title":"Maxima of a random model of the Riemann zeta function over intervals of varying length","author":[{"first_name":"Louis-Pierre","full_name":"Arguin, Louis-Pierre","last_name":"Arguin"},{"full_name":"Dubach, Guillaume","last_name":"Dubach","orcid":"0000-0001-6892-8137","id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E","first_name":"Guillaume"},{"full_name":"Hartung, Lisa","last_name":"Hartung","first_name":"Lisa"}],"citation":{"short":"L.-P. Arguin, G. Dubach, L. Hartung, ArXiv (n.d.).","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.","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>","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>.","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>","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>. ."},"publication":"arXiv","external_id":{"arxiv":["2103.04817"]},"day":"08","language":[{"iso":"eng"}]}]