[{"related_material":{"record":[{"id":"19540","relation":"dissertation_contains","status":"public"}]},"_id":"19548","isi":1,"date_published":"2025-01-09T00:00:00Z","language":[{"iso":"eng"}],"intvolume":"        15","DOAJ_listed":"1","publication_status":"published","department":[{"_id":"LaEr"},{"_id":"RoSe"}],"title":"Universal behavior of the BCS energy gap","doi":"10.4171/JST/540","oa_version":"Published Version","date_created":"2025-04-11T09:19:28Z","article_processing_charge":"No","type":"journal_article","arxiv":1,"file_date_updated":"2025-04-11T09:13:31Z","month":"01","abstract":[{"text":"We consider the BCS energy gap „.T / (essentially given by „.T / \u0019 .T; p\u0016/,\r\nthe BCS order parameter) at all temperatures 0 \u0014 T \u0014 Tc up to the critical one, Tc, and show\r\nthat, in the limit of weak coupling, the ratio „.T /=Tc is given by a universal function of the relative temperature T =Tc. On the one hand, this recovers a recent result by Langmann and Triola\r\n[Phys. Rev. B 108 (2023), no. 10, article no. 104503] on three-dimensional s-wave superconductors for temperatures bounded uniformly away from Tc. On the other hand, our result lifts these\r\nrestrictions, as we consider arbitrary spatial dimensions d 2 ¹1; 2; 3º, discuss superconductors\r\nwith non-zero angular momentum (primarily in two dimensions), and treat the perhaps physically most interesting (due to the occurrence of the superconducting phase transition) regime of\r\ntemperatures close to Tc.\r\n\r\n​\r\n .","lang":"eng"}],"external_id":{"arxiv":["2312.11310"],"isi":["001438931600009"]},"project":[{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"},{"name":"Mathematical Challenges in BCS Theory of Superconductivity","grant_number":"I06427","_id":"bda63fe5-d553-11ed-ba76-a16e3d2f256b"}],"publication_identifier":{"eissn":["1664-0403"]},"acknowledgement":"We thank Andreas Deuchert, Christian Hainzl, Edwin Langmann, Marius Lemm, Robert Seiringer, and Jan Philip Solovej for helpful discussions,\r\nand Edwin Langmann and Robert Seiringer for valuable comments on an earlier version of the manuscript.\r\nFunding. Joscha Henheik gratefully acknowledges partial financial support by the\r\nERC Advanced Grant “RMTBeyond” No. 101020331. Asbjørn Bækgaard Lauritsen\r\ngratefully acknowledges partial financial support by the Austrian Science Fund (FWF)\r\nthrough grant DOI 10.55776/I6427 (as part of the SFB/TRR 352).\r\n","corr_author":"1","author":[{"orcid":"0000-0003-1106-327X","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha","last_name":"Henheik","full_name":"Henheik, Sven Joscha"},{"orcid":"0000-0003-4476-2288","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1","full_name":"Lauritsen, Asbjørn Bækgaard","first_name":"Asbjørn Bækgaard","last_name":"Lauritsen"}],"year":"2025","date_updated":"2026-04-07T12:37:11Z","file":[{"date_updated":"2025-04-11T09:13:31Z","access_level":"open_access","date_created":"2025-04-11T09:13:31Z","success":1,"file_size":779158,"checksum":"f49e06e8dba819f7ad52a202e287ebca","content_type":"application/pdf","creator":"cchlebak","file_name":"Henheik_JSpectralTheory_2025.pdf","relation":"main_file","file_id":"19549"}],"publisher":"EMS Press","has_accepted_license":"1","scopus_import":"1","ec_funded":1,"publication":"Journal of Spectral Theory","status":"public","citation":{"mla":"Henheik, Sven Joscha, and Asbjørn Bækgaard Lauritsen. “Universal Behavior of the BCS Energy Gap.” <i>Journal of Spectral Theory</i>, vol. 15, no. 1, EMS Press, 2025, pp. 305–352, doi:<a href=\"https://doi.org/10.4171/JST/540\">10.4171/JST/540</a>.","ieee":"S. J. Henheik and A. B. Lauritsen, “Universal behavior of the BCS energy gap,” <i>Journal of Spectral Theory</i>, vol. 15, no. 1. EMS Press, pp. 305–352, 2025.","ama":"Henheik SJ, Lauritsen AB. Universal behavior of the BCS energy gap. <i>Journal of Spectral Theory</i>. 2025;15(1):305–352. doi:<a href=\"https://doi.org/10.4171/JST/540\">10.4171/JST/540</a>","apa":"Henheik, S. J., &#38; Lauritsen, A. B. (2025). Universal behavior of the BCS energy gap. <i>Journal of Spectral Theory</i>. EMS Press. <a href=\"https://doi.org/10.4171/JST/540\">https://doi.org/10.4171/JST/540</a>","short":"S.J. Henheik, A.B. Lauritsen, Journal of Spectral Theory 15 (2025) 305–352.","chicago":"Henheik, Sven Joscha, and Asbjørn Bækgaard Lauritsen. “Universal Behavior of the BCS Energy Gap.” <i>Journal of Spectral Theory</i>. EMS Press, 2025. <a href=\"https://doi.org/10.4171/JST/540\">https://doi.org/10.4171/JST/540</a>.","ista":"Henheik SJ, Lauritsen AB. 2025. Universal behavior of the BCS energy gap. Journal of Spectral Theory. 15(1), 305–352."},"ddc":["500"],"OA_type":"gold","page":"305–352","day":"09","OA_place":"publisher","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","volume":15,"issue":"1","article_type":"original","quality_controlled":"1","oa":1,"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"}},{"language":[{"iso":"eng"}],"publication_status":"published","intvolume":"        37","_id":"13975","isi":1,"date_published":"2024-03-01T00:00:00Z","external_id":{"arxiv":["2210.07927"],"isi":["001038341000001"]},"abstract":[{"lang":"eng","text":"We consider the spectrum of random Laplacian matrices of the form Ln=An−Dn where An\r\n is a real symmetric random matrix and Dn is a diagonal matrix whose entries are equal to the corresponding row sums of An. If An is a Wigner matrix with entries in the domain of attraction of a Gaussian distribution, the empirical spectral measure of Ln is known to converge to the free convolution of a semicircle distribution and a standard real Gaussian distribution. We consider real symmetric random matrices An with independent entries (up to symmetry) whose row sums converge to a purely non-Gaussian infinitely divisible distribution, which fall into the class of Lévy–Khintchine random matrices first introduced by Jung [Trans Am Math Soc, 370, (2018)]. Our main result shows that the empirical spectral measure of Ln  converges almost surely to a deterministic limit. A key step in the proof is to use the purely non-Gaussian nature of the row sums to build a random operator to which Ln converges in an appropriate sense. This operator leads to a recursive distributional equation uniquely describing the Stieltjes transform of the limiting empirical spectral measure."}],"month":"03","file_date_updated":"2024-07-22T09:41:21Z","arxiv":1,"type":"journal_article","corr_author":"1","acknowledgement":"The first author thanks Yizhe Zhu for pointing out reference [30]. We thank David Renfrew for comments on an earlier draft. We thank the anonymous referee for a careful reading and helpful comments.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria).","publication_identifier":{"eissn":["1572-9230"],"issn":["0894-9840"]},"department":[{"_id":"LaEr"}],"article_processing_charge":"Yes (via OA deal)","doi":"10.1007/s10959-023-01275-4","date_created":"2023-08-06T22:01:13Z","oa_version":"Published Version","title":"Spectrum of Lévy–Khintchine random laplacian matrices","has_accepted_license":"1","scopus_import":"1","file":[{"file_name":"2024_JourTheorProbab_Campbell.pdf","creator":"dernst","file_id":"17300","relation":"main_file","access_level":"open_access","date_updated":"2024-07-22T09:41:21Z","success":1,"date_created":"2024-07-22T09:41:21Z","content_type":"application/pdf","file_size":555070,"checksum":"f7793d313104c70422140c5e6494c779"}],"publisher":"Springer Nature","ddc":["510"],"citation":{"ama":"Campbell AJ, O’Rourke S. Spectrum of Lévy–Khintchine random laplacian matrices. <i>Journal of Theoretical Probability</i>. 2024;37:933-973. doi:<a href=\"https://doi.org/10.1007/s10959-023-01275-4\">10.1007/s10959-023-01275-4</a>","apa":"Campbell, A. J., &#38; O’Rourke, S. (2024). Spectrum of Lévy–Khintchine random laplacian matrices. <i>Journal of Theoretical Probability</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s10959-023-01275-4\">https://doi.org/10.1007/s10959-023-01275-4</a>","ieee":"A. J. Campbell and S. O’Rourke, “Spectrum of Lévy–Khintchine random laplacian matrices,” <i>Journal of Theoretical Probability</i>, vol. 37. Springer Nature, pp. 933–973, 2024.","mla":"Campbell, Andrew J., and Sean O’Rourke. “Spectrum of Lévy–Khintchine Random Laplacian Matrices.” <i>Journal of Theoretical Probability</i>, vol. 37, Springer Nature, 2024, pp. 933–73, doi:<a href=\"https://doi.org/10.1007/s10959-023-01275-4\">10.1007/s10959-023-01275-4</a>.","ista":"Campbell AJ, O’Rourke S. 2024. Spectrum of Lévy–Khintchine random laplacian matrices. Journal of Theoretical Probability. 37, 933–973.","chicago":"Campbell, Andrew J, and Sean O’Rourke. “Spectrum of Lévy–Khintchine Random Laplacian Matrices.” <i>Journal of Theoretical Probability</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s10959-023-01275-4\">https://doi.org/10.1007/s10959-023-01275-4</a>.","short":"A.J. Campbell, S. O’Rourke, Journal of Theoretical Probability 37 (2024) 933–973."},"page":"933-973","status":"public","publication":"Journal of Theoretical Probability","year":"2024","author":[{"full_name":"Campbell, Andrew J","first_name":"Andrew J","last_name":"Campbell","id":"582b06a9-1f1c-11ee-b076-82ffce00dde4"},{"full_name":"O’Rourke, Sean","first_name":"Sean","last_name":"O’Rourke"}],"date_updated":"2024-07-22T09:41:42Z","oa":1,"quality_controlled":"1","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"01","volume":37},{"language":[{"iso":"eng"}],"intvolume":"       188","publication_status":"published","_id":"14408","isi":1,"date_published":"2024-04-01T00:00:00Z","external_id":{"arxiv":["2210.12060"],"isi":["001118972500001"]},"project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020"}],"arxiv":1,"type":"journal_article","month":"04","abstract":[{"lang":"eng","text":"We prove that the mesoscopic linear statistics ∑if(na(σi−z0)) of the eigenvalues {σi}i of large n×n non-Hermitian random matrices with complex centred i.i.d. entries are asymptotically Gaussian for any H20-functions f around any point z0 in the bulk of the spectrum on any mesoscopic scale 0<a<1/2. This extends our previous result (Cipolloni et al. in Commun Pure Appl Math, 2019. arXiv:1912.04100), that was valid on the macroscopic scale, a=0\r\n, to cover the entire mesoscopic regime. The main novelty is a local law for the product of resolvents for the Hermitization of X at spectral parameters z1,z2 with an improved error term in the entire mesoscopic regime |z1−z2|≫n−1/2. The proof is dynamical; it relies on a recursive tandem of the characteristic flow method and the Green function comparison idea combined with a separation of the unstable mode of the underlying stability operator."}],"acknowledgement":"The authors are grateful to Joscha Henheik for his help with the formulas in Appendix B.\r\nLászló Erdős supported by ERC Advanced Grant “RMTBeyond” No. 101020331. Dominik Schröder supported by the SNSF Ambizione Grant PZ00P2 209089.","publication_identifier":{"eissn":["1432-2064"],"issn":["0178-8051"]},"department":[{"_id":"LaEr"}],"doi":"10.1007/s00440-023-01229-1","oa_version":"Preprint","date_created":"2023-10-08T22:01:17Z","article_processing_charge":"No","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2210.12060"}],"title":"Mesoscopic central limit theorem for non-Hermitian random matrices","publisher":"Springer Nature","scopus_import":"1","ec_funded":1,"citation":{"apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2024). Mesoscopic central limit theorem for non-Hermitian random matrices. <i>Probability Theory and Related Fields</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00440-023-01229-1\">https://doi.org/10.1007/s00440-023-01229-1</a>","ama":"Cipolloni G, Erdös L, Schröder DJ. Mesoscopic central limit theorem for non-Hermitian random matrices. <i>Probability Theory and Related Fields</i>. 2024;188:1131-1182. doi:<a href=\"https://doi.org/10.1007/s00440-023-01229-1\">10.1007/s00440-023-01229-1</a>","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Mesoscopic central limit theorem for non-Hermitian random matrices,” <i>Probability Theory and Related Fields</i>, vol. 188. Springer Nature, pp. 1131–1182, 2024.","mla":"Cipolloni, Giorgio, et al. “Mesoscopic Central Limit Theorem for Non-Hermitian Random Matrices.” <i>Probability Theory and Related Fields</i>, vol. 188, Springer Nature, 2024, pp. 1131–82, doi:<a href=\"https://doi.org/10.1007/s00440-023-01229-1\">10.1007/s00440-023-01229-1</a>.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2024. Mesoscopic central limit theorem for non-Hermitian random matrices. Probability Theory and Related Fields. 188, 1131–1182.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Mesoscopic Central Limit Theorem for Non-Hermitian Random Matrices.” <i>Probability Theory and Related Fields</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s00440-023-01229-1\">https://doi.org/10.1007/s00440-023-01229-1</a>.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Probability Theory and Related Fields 188 (2024) 1131–1182."},"page":"1131-1182","status":"public","publication":"Probability Theory and Related Fields","author":[{"orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio","last_name":"Cipolloni","first_name":"Giorgio"},{"full_name":"Erdös, László","last_name":"Erdös","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856","first_name":"Dominik J","last_name":"Schröder","full_name":"Schröder, Dominik J"}],"year":"2024","date_updated":"2025-08-05T13:28:15Z","oa":1,"article_type":"original","quality_controlled":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"01","volume":188},{"date_published":"2024-12-20T00:00:00Z","isi":1,"_id":"18762","related_material":{"record":[{"relation":"earlier_version","id":"17173","status":"public"}]},"DOAJ_listed":"1","publication_status":"published","intvolume":"        29","language":[{"iso":"eng"}],"article_processing_charge":"Yes","doi":"10.1214/24-EJP1247","date_created":"2025-01-05T23:01:58Z","oa_version":"Published Version","title":"Multi-point functional central limit theorem for Wigner matrices","department":[{"_id":"LaEr"}],"corr_author":"1","acknowledgement":"I am very grateful to László Erdős for suggesting the topic and many valuable discussions during my work on the project. I would also like to thank the two anonymous referees for their careful reading of the manuscript and detailed feedback.\r\nPartially supported by ERC Advanced Grants “RMTBeyond” No. 101020331 and “LDRaM” No. 884584.","publication_identifier":{"eissn":["1083-6489"]},"project":[{"call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331"}],"external_id":{"arxiv":["2307.11028"],"isi":["001381599200001"]},"abstract":[{"text":"Consider the random variable $\\mathrm{Tr}( f_1(W)A_1\\dots f_k(W)A_k)$ where $W$ is an $N\\times N$ Hermitian Wigner matrix, $k\\in\\mathbb{N}$, and choose (possibly $N$-dependent) regular functions $f_1,\\dots, f_k$ as well as bounded deterministic matrices $A_1,\\dots,A_k$. We give a functional central limit theorem showing that the fluctuations around the expectation are Gaussian. Moreover, we determine the limiting covariance structure and give explicit error bounds in terms of the scaling of $f_1,\\dots,f_k$ and the number of traceless matrices among $A_1,\\dots,A_k$, thus extending the results of [Cipolloni, Erdős, Schröder 2023] to products of arbitrary length $k\\geq2$. As an application, we consider the fluctuation of $\\mathrm{Tr}(\\mathrm{e}^{\\mathrm{i} tW}A_1\\mathrm{e}^{-\\mathrm{i} tW}A_2)$ around its thermal value $\\mathrm{Tr}(A_1)\\mathrm{Tr}(A_2)$ when $t$ is large and give an explicit formula for the variance.","lang":"eng"}],"arxiv":1,"file_date_updated":"2025-01-08T08:44:03Z","month":"12","type":"journal_article","date_updated":"2025-09-09T11:59:15Z","year":"2024","author":[{"full_name":"Reker, Jana","first_name":"Jana","last_name":"Reker","id":"e796e4f9-dc8d-11ea-abe3-97e26a0323e9"}],"ddc":["510"],"OA_type":"gold","citation":{"mla":"Reker, Jana. “Multi-Point Functional Central Limit Theorem for Wigner Matrices.” <i>Electronic Journal of Probability</i>, vol. 29, 191, Institute of Mathematical Statistics, 2024, doi:<a href=\"https://doi.org/10.1214/24-EJP1247\">10.1214/24-EJP1247</a>.","ieee":"J. Reker, “Multi-point functional central limit theorem for Wigner matrices,” <i>Electronic Journal of Probability</i>, vol. 29. Institute of Mathematical Statistics, 2024.","ama":"Reker J. Multi-point functional central limit theorem for Wigner matrices. <i>Electronic Journal of Probability</i>. 2024;29. doi:<a href=\"https://doi.org/10.1214/24-EJP1247\">10.1214/24-EJP1247</a>","apa":"Reker, J. (2024). Multi-point functional central limit theorem for Wigner matrices. <i>Electronic Journal of Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/24-EJP1247\">https://doi.org/10.1214/24-EJP1247</a>","short":"J. Reker, Electronic Journal of Probability 29 (2024).","chicago":"Reker, Jana. “Multi-Point Functional Central Limit Theorem for Wigner Matrices.” <i>Electronic Journal of Probability</i>. Institute of Mathematical Statistics, 2024. <a href=\"https://doi.org/10.1214/24-EJP1247\">https://doi.org/10.1214/24-EJP1247</a>.","ista":"Reker J. 2024. Multi-point functional central limit theorem for Wigner matrices. Electronic Journal of Probability. 29, 191."},"article_number":"191","publication":"Electronic Journal of Probability","status":"public","ec_funded":1,"scopus_import":"1","has_accepted_license":"1","publisher":"Institute of Mathematical Statistics","file":[{"file_name":"2024_ElectrJournProbability_Reker.pdf","creator":"dernst","file_id":"18773","relation":"main_file","file_size":812428,"content_type":"application/pdf","checksum":"67178feaa8630a332599d3037a3fe70e","date_updated":"2025-01-08T08:44:03Z","access_level":"open_access","date_created":"2025-01-08T08:44:03Z","success":1}],"volume":29,"OA_place":"publisher","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","day":"20","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"oa":1,"quality_controlled":"1","article_type":"original"},{"year":"2024","author":[{"full_name":"Erdös, László","last_name":"Erdös","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603"},{"id":"b0cc634c-d549-11ee-96c8-87338c7ad808","orcid":"0000-0003-2625-495X","first_name":"Benjamin","last_name":"McKenna","full_name":"McKenna, Benjamin"}],"date_updated":"2025-09-04T12:08:11Z","ec_funded":1,"scopus_import":"1","publisher":"Institute of Mathematical Statistics","page":"1623-1662","citation":{"short":"L. Erdös, B. McKenna, Annals of Applied Probability 34 (2024) 1623–1662.","ista":"Erdös L, McKenna B. 2024. Extremal statistics of quadratic forms of GOE/GUE eigenvectors. Annals of Applied Probability. 34(1B), 1623–1662.","chicago":"Erdös, László, and Benjamin McKenna. “Extremal Statistics of Quadratic Forms of GOE/GUE Eigenvectors.” <i>Annals of Applied Probability</i>. Institute of Mathematical Statistics, 2024. <a href=\"https://doi.org/10.1214/23-AAP2000\">https://doi.org/10.1214/23-AAP2000</a>.","mla":"Erdös, László, and Benjamin McKenna. “Extremal Statistics of Quadratic Forms of GOE/GUE Eigenvectors.” <i>Annals of Applied Probability</i>, vol. 34, no. 1B, Institute of Mathematical Statistics, 2024, pp. 1623–62, doi:<a href=\"https://doi.org/10.1214/23-AAP2000\">10.1214/23-AAP2000</a>.","ieee":"L. Erdös and B. McKenna, “Extremal statistics of quadratic forms of GOE/GUE eigenvectors,” <i>Annals of Applied Probability</i>, vol. 34, no. 1B. Institute of Mathematical Statistics, pp. 1623–1662, 2024.","ama":"Erdös L, McKenna B. Extremal statistics of quadratic forms of GOE/GUE eigenvectors. <i>Annals of Applied Probability</i>. 2024;34(1B):1623-1662. doi:<a href=\"https://doi.org/10.1214/23-AAP2000\">10.1214/23-AAP2000</a>","apa":"Erdös, L., &#38; McKenna, B. (2024). Extremal statistics of quadratic forms of GOE/GUE eigenvectors. <i>Annals of Applied Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/23-AAP2000\">https://doi.org/10.1214/23-AAP2000</a>"},"status":"public","publication":"Annals of Applied Probability","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","day":"01","issue":"1B","volume":34,"oa":1,"quality_controlled":"1","article_type":"original","isi":1,"_id":"15025","date_published":"2024-02-01T00:00:00Z","language":[{"iso":"eng"}],"publication_status":"published","intvolume":"        34","department":[{"_id":"LaEr"}],"article_processing_charge":"No","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2208.12206","open_access":"1"}],"oa_version":"Preprint","doi":"10.1214/23-AAP2000","date_created":"2024-02-25T23:00:56Z","title":"Extremal statistics of quadratic forms of GOE/GUE eigenvectors","project":[{"call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"external_id":{"arxiv":["2208.12206"],"isi":["001163006100021"]},"abstract":[{"lang":"eng","text":"We consider quadratic forms of deterministic matrices A evaluated at the random eigenvectors of a large N×N GOE or GUE matrix, or equivalently evaluated at the columns of a Haar-orthogonal or Haar-unitary random matrix. We prove that, as long as the deterministic matrix has rank much smaller than √N, the distributions of the extrema of these quadratic forms are asymptotically the same as if the eigenvectors were independent Gaussians. This reduces the problem to Gaussian computations, which we carry out in several cases to illustrate our result, finding Gumbel or Weibull limiting distributions depending on the signature of A. Our result also naturally applies to the eigenvectors of any invariant ensemble."}],"arxiv":1,"month":"02","type":"journal_article","corr_author":"1","acknowledgement":"The first author was supported by the ERC Advanced Grant “RMTBeyond” No. 101020331. The second author was supported by Fulbright Austria and the Austrian Marshall Plan Foundation.","publication_identifier":{"issn":["1050-5164"]}},{"language":[{"iso":"eng"}],"intvolume":"        77","publication_status":"published","isi":1,"_id":"15378","date_published":"2024-09-01T00:00:00Z","month":"09","arxiv":1,"file_date_updated":"2025-01-09T09:36:41Z","type":"journal_article","abstract":[{"text":"We consider N×N non-Hermitian random matrices of the form X+A, where A is a general deterministic matrix and N−−√X consists of independent entries with zero mean, unit variance, and bounded densities. For this ensemble, we prove (i) a Wegner estimate, i.e. that the local density of eigenvalues is bounded by N1+o(1) and (ii) that the expected condition number of any bulk eigenvalue is bounded by N1+o(1); both results are optimal up to the factor No(1). The latter result complements the very recent matching lower bound obtained in [15] (arXiv:2301.03549) and improves the N-dependence of the upper bounds in [5,6,32] (arXiv:1906.11819, arXiv:2005.08930, arXiv:2005.08908). Our main ingredient, a near-optimal lower tail estimate for the small singular values of X+A−z, is of independent interest.","lang":"eng"}],"external_id":{"isi":["001217139900001"],"arxiv":["2301.04981"]},"project":[{"call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"publication_identifier":{"eissn":["1097-0312"],"issn":["0010-3640"]},"acknowledgement":"László Erdős is partially supported by ERC Advanced Grant “RMTBeyond” No. 101020331. Hong Chang Ji is supported by ERC Advanced Grant “RMTBeyond” No. 101020331.","corr_author":"1","department":[{"_id":"LaEr"}],"title":"Wegner estimate and upper bound on the eigenvalue condition number of non-Hermitian random matrices","doi":"10.1002/cpa.22201","date_created":"2024-05-12T22:01:02Z","oa_version":"Published Version","article_processing_charge":"Yes (via OA deal)","file":[{"creator":"dernst","file_name":"2024_CommPureApplMath_Erdoes.pdf","relation":"main_file","file_id":"18803","checksum":"fbcc9cc7bf274f024e4f4afc9c208f96","content_type":"application/pdf","file_size":566963,"date_updated":"2025-01-09T09:36:41Z","access_level":"open_access","date_created":"2025-01-09T09:36:41Z","success":1}],"publisher":"Wiley","scopus_import":"1","ec_funded":1,"has_accepted_license":"1","publication":"Communications on Pure and Applied Mathematics","status":"public","ddc":["510"],"page":"3785-3840","OA_type":"hybrid","citation":{"ama":"Erdös L, Ji HC. Wegner estimate and upper bound on the eigenvalue condition number of non-Hermitian random matrices. <i>Communications on Pure and Applied Mathematics</i>. 2024;77(9):3785-3840. doi:<a href=\"https://doi.org/10.1002/cpa.22201\">10.1002/cpa.22201</a>","ieee":"L. Erdös and H. C. Ji, “Wegner estimate and upper bound on the eigenvalue condition number of non-Hermitian random matrices,” <i>Communications on Pure and Applied Mathematics</i>, vol. 77, no. 9. Wiley, pp. 3785–3840, 2024.","apa":"Erdös, L., &#38; Ji, H. C. (2024). Wegner estimate and upper bound on the eigenvalue condition number of non-Hermitian random matrices. <i>Communications on Pure and Applied Mathematics</i>. Wiley. <a href=\"https://doi.org/10.1002/cpa.22201\">https://doi.org/10.1002/cpa.22201</a>","mla":"Erdös, László, and Hong Chang Ji. “Wegner Estimate and Upper Bound on the Eigenvalue Condition Number of Non-Hermitian Random Matrices.” <i>Communications on Pure and Applied Mathematics</i>, vol. 77, no. 9, Wiley, 2024, pp. 3785–840, doi:<a href=\"https://doi.org/10.1002/cpa.22201\">10.1002/cpa.22201</a>.","chicago":"Erdös, László, and Hong Chang Ji. “Wegner Estimate and Upper Bound on the Eigenvalue Condition Number of Non-Hermitian Random Matrices.” <i>Communications on Pure and Applied Mathematics</i>. Wiley, 2024. <a href=\"https://doi.org/10.1002/cpa.22201\">https://doi.org/10.1002/cpa.22201</a>.","ista":"Erdös L, Ji HC. 2024. Wegner estimate and upper bound on the eigenvalue condition number of non-Hermitian random matrices. Communications on Pure and Applied Mathematics. 77(9), 3785–3840.","short":"L. Erdös, H.C. Ji, Communications on Pure and Applied Mathematics 77 (2024) 3785–3840."},"author":[{"full_name":"Erdös, László","last_name":"Erdös","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603"},{"id":"dd216c0a-c1f9-11eb-beaf-e9ea9d2de76d","last_name":"Ji","first_name":"Hong Chang","full_name":"Ji, Hong Chang"}],"year":"2024","date_updated":"2025-09-08T07:25:47Z","article_type":"original","quality_controlled":"1","oa":1,"tmp":{"name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","short":"CC BY-NC-ND (4.0)","image":"/images/cc_by_nc_nd.png","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode"},"day":"01","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","OA_place":"publisher","volume":77,"issue":"9"},{"file":[{"content_type":"application/pdf","file_size":1233508,"checksum":"f36a7dbf53f23d5833db711052e69b49","access_level":"open_access","date_updated":"2024-07-22T06:40:19Z","date_created":"2024-07-22T06:40:19Z","success":1,"file_name":"2024_IMRN_Campbell.pdf","creator":"dernst","file_id":"17288","relation":"main_file"}],"publisher":"Oxford University Press","scopus_import":"1","has_accepted_license":"1","ddc":["510"],"page":"10189-10218","citation":{"chicago":"Campbell, Andrew J, Sean O’Rourke, and David T Renfrew. “The Fractional Free Convolution of R-Diagonal Elements and Random Polynomials under Repeated Differentiation.” <i>International Mathematics Research Notices</i>. Oxford University Press, 2024. <a href=\"https://doi.org/10.1093/imrn/rnae062\">https://doi.org/10.1093/imrn/rnae062</a>.","short":"A.J. Campbell, S. O’Rourke, D.T. Renfrew, International Mathematics Research Notices 2024 (2024) 10189–10218.","ista":"Campbell AJ, O’Rourke S, Renfrew DT. 2024. The fractional free convolution of R-diagonal elements and random polynomials under repeated differentiation. International Mathematics Research Notices. 2024(13), 10189–10218.","apa":"Campbell, A. J., O’Rourke, S., &#38; Renfrew, D. T. (2024). The fractional free convolution of R-diagonal elements and random polynomials under repeated differentiation. <i>International Mathematics Research Notices</i>. Oxford University Press. <a href=\"https://doi.org/10.1093/imrn/rnae062\">https://doi.org/10.1093/imrn/rnae062</a>","ieee":"A. J. Campbell, S. O’Rourke, and D. T. Renfrew, “The fractional free convolution of R-diagonal elements and random polynomials under repeated differentiation,” <i>International Mathematics Research Notices</i>, vol. 2024, no. 13. Oxford University Press, pp. 10189–10218, 2024.","ama":"Campbell AJ, O’Rourke S, Renfrew DT. The fractional free convolution of R-diagonal elements and random polynomials under repeated differentiation. <i>International Mathematics Research Notices</i>. 2024;2024(13):10189-10218. doi:<a href=\"https://doi.org/10.1093/imrn/rnae062\">10.1093/imrn/rnae062</a>","mla":"Campbell, Andrew J., et al. “The Fractional Free Convolution of R-Diagonal Elements and Random Polynomials under Repeated Differentiation.” <i>International Mathematics Research Notices</i>, vol. 2024, no. 13, Oxford University Press, 2024, pp. 10189–218, doi:<a href=\"https://doi.org/10.1093/imrn/rnae062\">10.1093/imrn/rnae062</a>."},"status":"public","publication":"International Mathematics Research Notices","author":[{"full_name":"Campbell, Andrew J","last_name":"Campbell","first_name":"Andrew J","id":"582b06a9-1f1c-11ee-b076-82ffce00dde4"},{"full_name":"O'Rourke, Sean","first_name":"Sean","last_name":"O'Rourke"},{"orcid":"0000-0003-3493-121X","id":"4845BF6A-F248-11E8-B48F-1D18A9856A87","full_name":"Renfrew, David T","first_name":"David T","last_name":"Renfrew"}],"year":"2024","date_updated":"2025-09-08T08:16:32Z","oa":1,"article_type":"original","quality_controlled":"1","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","day":"01","issue":"13","volume":2024,"language":[{"iso":"eng"}],"intvolume":"      2024","publication_status":"published","_id":"17281","isi":1,"date_published":"2024-07-01T00:00:00Z","external_id":{"isi":["001198019500001"]},"type":"journal_article","file_date_updated":"2024-07-22T06:40:19Z","month":"07","abstract":[{"text":"We extend the free convolution of Brown measures of R-diagonal elements introduced by Kösters and Tikhomirov [ 28] to fractional powers. We then show how this fractional free convolution arises naturally when studying the roots of random polynomials with independent coefficients under repeated differentiation. When the proportion of derivatives to the degree approaches one, we establish central limit theorem-type behavior and discuss stable distributions.","lang":"eng"}],"acknowledgement":"This work was supported by the National Science Foundation [Grant No. DMS-2143142 to S.O.]; and the European Research Council [Grant No. 101020331].The third author acknowledges the support of the University of Colorado Boulder, where a portion of this work was completed. The authors thank Martin Auer, Vadim Gorin, Brian Hall, and Noah Williams for comments, corrections, and references. The authors also wish to thank the anonymous referees for useful feedback and corrections.","corr_author":"1","publication_identifier":{"eissn":["1687-0247"],"issn":["1073-7928"]},"department":[{"_id":"LaEr"}],"date_created":"2024-07-21T22:01:01Z","doi":"10.1093/imrn/rnae062","oa_version":"Published Version","article_processing_charge":"Yes (via OA deal)","title":"The fractional free convolution of R-diagonal elements and random polynomials under repeated differentiation"},{"publication_status":"published","intvolume":"        65","language":[{"iso":"eng"}],"date_published":"2024-06-01T00:00:00Z","_id":"17375","isi":1,"corr_author":"1","acknowledgement":"L.E. and Y.X. were supported by the ERC Advanced Grant “RMTBeyond” Grant No. 101020331.","publication_identifier":{"issn":["0022-2488"]},"project":[{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"}],"external_id":{"arxiv":["2210.15643"],"isi":["001252240700002"]},"abstract":[{"lang":"eng","text":"We consider the spectral radius of a large random matrix X with independent, identically distributed entries. We show that its typical size is given by a precise three-term asymptotics with an optimal error term beyond the radius of the celebrated circular law. The coefficients in this asymptotics are universal but they differ from a similar asymptotics recently proved for the rightmost eigenvalue of X in Cipolloni et al., Ann. Probab. 51(6), 2192–2242 (2023). To access the more complicated spectral radius, we need to establish a new decorrelation mechanism for the low-lying singular values of X − z for different complex shift parameters z using the Dyson Brownian Motion."}],"arxiv":1,"type":"journal_article","month":"06","article_processing_charge":"No","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2210.15643"}],"oa_version":"Preprint","date_created":"2024-08-04T22:01:22Z","doi":"10.1063/5.0209705","title":"Precise asymptotics for the spectral radius of a large random matrix","department":[{"_id":"LaEr"}],"citation":{"ieee":"G. Cipolloni, L. Erdös, and Y. Xu, “Precise asymptotics for the spectral radius of a large random matrix,” <i>Journal of Mathematical Physics</i>, vol. 65, no. 6. AIP Publishing, 2024.","ama":"Cipolloni G, Erdös L, Xu Y. Precise asymptotics for the spectral radius of a large random matrix. <i>Journal of Mathematical Physics</i>. 2024;65(6). doi:<a href=\"https://doi.org/10.1063/5.0209705\">10.1063/5.0209705</a>","apa":"Cipolloni, G., Erdös, L., &#38; Xu, Y. (2024). Precise asymptotics for the spectral radius of a large random matrix. <i>Journal of Mathematical Physics</i>. AIP Publishing. <a href=\"https://doi.org/10.1063/5.0209705\">https://doi.org/10.1063/5.0209705</a>","mla":"Cipolloni, Giorgio, et al. “Precise Asymptotics for the Spectral Radius of a Large Random Matrix.” <i>Journal of Mathematical Physics</i>, vol. 65, no. 6, 063302, AIP Publishing, 2024, doi:<a href=\"https://doi.org/10.1063/5.0209705\">10.1063/5.0209705</a>.","ista":"Cipolloni G, Erdös L, Xu Y. 2024. Precise asymptotics for the spectral radius of a large random matrix. Journal of Mathematical Physics. 65(6), 063302.","short":"G. Cipolloni, L. Erdös, Y. Xu, Journal of Mathematical Physics 65 (2024).","chicago":"Cipolloni, Giorgio, László Erdös, and Yuanyuan Xu. “Precise Asymptotics for the Spectral Radius of a Large Random Matrix.” <i>Journal of Mathematical Physics</i>. AIP Publishing, 2024. <a href=\"https://doi.org/10.1063/5.0209705\">https://doi.org/10.1063/5.0209705</a>."},"article_number":"063302","status":"public","publication":"Journal of Mathematical Physics","ec_funded":1,"scopus_import":"1","publisher":"AIP Publishing","date_updated":"2025-09-08T08:44:57Z","year":"2024","author":[{"orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio","last_name":"Cipolloni","full_name":"Cipolloni, Giorgio"},{"full_name":"Erdös, László","first_name":"László","last_name":"Erdös","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Xu, Yuanyuan","first_name":"Yuanyuan","last_name":"Xu","orcid":"0000-0003-1559-1205","id":"7902bdb1-a2a4-11eb-a164-c9216f71aea3"}],"oa":1,"quality_controlled":"1","article_type":"original","issue":"6","volume":65,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","day":"01"},{"OA_place":"publisher","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","day":"01","issue":"12","volume":405,"oa":1,"quality_controlled":"1","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"year":"2024","author":[{"last_name":"Erdös","first_name":"László","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603"},{"full_name":"Riabov, Volodymyr","first_name":"Volodymyr","last_name":"Riabov","id":"1949f904-edfb-11eb-afb5-e2dfddabb93b"}],"date_updated":"2026-04-07T12:32:19Z","scopus_import":"1","has_accepted_license":"1","publisher":"Springer Nature","file":[{"file_name":"2024_CommMathPhysics_Erdoes.pdf","creator":"dernst","file_id":"18562","relation":"main_file","content_type":"application/pdf","file_size":1426046,"checksum":"c9ae0ea195bd39b8b3a630d492fb00dc","access_level":"open_access","date_updated":"2024-11-18T08:15:07Z","success":1,"date_created":"2024-11-18T08:15:07Z"}],"article_number":"282","OA_type":"hybrid","citation":{"ista":"Erdös L, Riabov V. 2024. Eigenstate Thermalization Hypothesis for Wigner-type matrices. Communications in Mathematical Physics. 405(12), 282.","short":"L. Erdös, V. Riabov, Communications in Mathematical Physics 405 (2024).","chicago":"Erdös, László, and Volodymyr Riabov. “Eigenstate Thermalization Hypothesis for Wigner-Type Matrices.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s00220-024-05143-y\">https://doi.org/10.1007/s00220-024-05143-y</a>.","apa":"Erdös, L., &#38; Riabov, V. (2024). Eigenstate Thermalization Hypothesis for Wigner-type matrices. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-024-05143-y\">https://doi.org/10.1007/s00220-024-05143-y</a>","ieee":"L. Erdös and V. Riabov, “Eigenstate Thermalization Hypothesis for Wigner-type matrices,” <i>Communications in Mathematical Physics</i>, vol. 405, no. 12. Springer Nature, 2024.","mla":"Erdös, László, and Volodymyr Riabov. “Eigenstate Thermalization Hypothesis for Wigner-Type Matrices.” <i>Communications in Mathematical Physics</i>, vol. 405, no. 12, 282, Springer Nature, 2024, doi:<a href=\"https://doi.org/10.1007/s00220-024-05143-y\">10.1007/s00220-024-05143-y</a>.","ama":"Erdös L, Riabov V. Eigenstate Thermalization Hypothesis for Wigner-type matrices. <i>Communications in Mathematical Physics</i>. 2024;405(12). doi:<a href=\"https://doi.org/10.1007/s00220-024-05143-y\">10.1007/s00220-024-05143-y</a>"},"ddc":["510"],"publication":"Communications in Mathematical Physics","status":"public","department":[{"_id":"LaEr"}],"article_processing_charge":"Yes (via OA deal)","oa_version":"Published Version","doi":"10.1007/s00220-024-05143-y","date_created":"2024-11-17T23:01:46Z","title":"Eigenstate Thermalization Hypothesis for Wigner-type matrices","external_id":{"isi":["001348943900004"],"arxiv":["2403.10359"],"pmid":["39526190"]},"abstract":[{"lang":"eng","text":"We prove the Eigenstate Thermalization Hypothesis for general Wigner-type matrices in the bulk of the self-consistent spectrum, with optimal control on the fluctuations for obs ervables of arbitrary rank. As the main technical ingredient, we prove rank-uniform optimal local laws for one and two resolvents of a Wigner-type matrix with regular observables. Our results hold under very general conditions on the variance profile, even allowing many vanishing entries, demonstrating that Eigenstate Thermalization occurs robustly across a diverse class of random matrix ensembles, for which the underlying quantum system has a non-trivial spatial structure."}],"month":"12","file_date_updated":"2024-11-18T08:15:07Z","type":"journal_article","arxiv":1,"corr_author":"1","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria).","publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"_id":"18554","related_material":{"record":[{"relation":"dissertation_contains","id":"20575","status":"public"}]},"isi":1,"date_published":"2024-12-01T00:00:00Z","language":[{"iso":"eng"}],"pmid":1,"publication_status":"published","intvolume":"       405"},{"article_type":"original","quality_controlled":"1","oa":1,"volume":28,"issue":"6","day":"30","OA_place":"repository","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","publication":"Advances in Theoretical and Mathematical Physics","page":"2025-2083","citation":{"ama":"Cipolloni G, Erdös L, Henheik SJ. Out-of-time-ordered correlators for Wigner matrices. <i>Advances in Theoretical and Mathematical Physics</i>. 2024;28(6):2025-2083. doi:<a href=\"https://doi.org/10.4310/ATMP.241031013250\">10.4310/ATMP.241031013250</a>","ieee":"G. Cipolloni, L. Erdös, and S. J. Henheik, “Out-of-time-ordered correlators for Wigner matrices,” <i>Advances in Theoretical and Mathematical Physics</i>, vol. 28, no. 6. International Press, pp. 2025–2083, 2024.","apa":"Cipolloni, G., Erdös, L., &#38; Henheik, S. J. (2024). Out-of-time-ordered correlators for Wigner matrices. <i>Advances in Theoretical and Mathematical Physics</i>. International Press. <a href=\"https://doi.org/10.4310/ATMP.241031013250\">https://doi.org/10.4310/ATMP.241031013250</a>","mla":"Cipolloni, Giorgio, et al. “Out-of-Time-Ordered Correlators for Wigner Matrices.” <i>Advances in Theoretical and Mathematical Physics</i>, vol. 28, no. 6, International Press, 2024, pp. 2025–83, doi:<a href=\"https://doi.org/10.4310/ATMP.241031013250\">10.4310/ATMP.241031013250</a>.","ista":"Cipolloni G, Erdös L, Henheik SJ. 2024. Out-of-time-ordered correlators for Wigner matrices. Advances in Theoretical and Mathematical Physics. 28(6), 2025–2083.","chicago":"Cipolloni, Giorgio, László Erdös, and Sven Joscha Henheik. “Out-of-Time-Ordered Correlators for Wigner Matrices.” <i>Advances in Theoretical and Mathematical Physics</i>. International Press, 2024. <a href=\"https://doi.org/10.4310/ATMP.241031013250\">https://doi.org/10.4310/ATMP.241031013250</a>.","short":"G. Cipolloni, L. Erdös, S.J. Henheik, Advances in Theoretical and Mathematical Physics 28 (2024) 2025–2083."},"OA_type":"green","publisher":"International Press","ec_funded":1,"scopus_import":"1","date_updated":"2026-04-07T12:37:10Z","author":[{"last_name":"Cipolloni","first_name":"Giorgio","full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Erdös","first_name":"László","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603"},{"full_name":"Henheik, Sven Joscha","first_name":"Sven Joscha","last_name":"Henheik","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","orcid":"0000-0003-1106-327X"}],"year":"2024","publication_identifier":{"eissn":["1095-0753"],"issn":["1095-0761"]},"acknowledgement":"LE and JH were supported by the ERC Advanced Grant łRMTBeyondž No. 101020331","corr_author":"1","month":"10","arxiv":1,"type":"journal_article","abstract":[{"text":"We consider the time evolution of the out-of-time-ordered correlator (OTOC) of two general observables \r\n and \r\n in a mean field chaotic quantum system described by a random Wigner matrix as its Hamiltonian. We rigorously identify three time regimes separated by the physically relevant scrambling and relaxation times. The main feature of our analysis is that we express the error terms in the optimal Schatten (tracial) norms of the observables, allowing us to track the exact dependence of the errors on their rank. In particular, for significantly overlapping observables with low rank the OTOC is shown to exhibit a significant local maximum at the scrambling time, a feature that may not have been noticed in the physics literature before. Our main tool is a novel multi-resolvent local law with Schatten norms that unifies and improves previous local laws involving either the much cruder operator norm (cf. [10]) or the Hilbert-Schmidt norm (cf. [11]).","lang":"eng"}],"external_id":{"arxiv":["2402.17609"]},"project":[{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"}],"title":"Out-of-time-ordered correlators for Wigner matrices","date_created":"2024-12-15T23:01:51Z","oa_version":"Preprint","doi":"10.4310/ATMP.241031013250","article_processing_charge":"No","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2402.17609","open_access":"1"}],"department":[{"_id":"LaEr"}],"intvolume":"        28","publication_status":"published","language":[{"iso":"eng"}],"date_published":"2024-10-30T00:00:00Z","_id":"18656","related_material":{"record":[{"id":"19540","relation":"dissertation_contains","status":"public"}]}},{"publication_status":"published","intvolume":"       287","language":[{"iso":"eng"}],"date_published":"2024-08-15T00:00:00Z","related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"19540"}]},"_id":"17049","isi":1,"publication_identifier":{"issn":["0022-1236"],"eissn":["1096-0783"]},"corr_author":"1","acknowledgement":"Supported by ERC Advanced Grant “RMTBeyond” No. 101020331.\r\nSupported by the SNSF Ambizione Grant PZ00P2_209089.","abstract":[{"lang":"eng","text":"We consider large non-Hermitian NxN matrices with an additive independent, identically distributed (i.i.d.) noise for each matrix elements. We show that already a small noise of variance 1/N completely thermalises the bulk singular vectors, in particular they satisfy the strong form of Quantum Unique Ergodicity (QUE) with an optimal speed of convergence. In physics terms, we thus extend the Eigenstate Thermalisation Hypothesis, formulated originally by Deutsch [34] and proven for Wigner matrices in [23], to arbitrary non-Hermitian matrices with an i.i.d. noise. As a consequence we obtain an optimal lower bound on the diagonal overlaps of the corresponding non-Hermitian eigenvectors. This quantity, also known as the (square of the) eigenvalue condition number measuring the sensitivity of the eigenvalue to small perturbations, has notoriously escaped rigorous treatment beyond the explicitly computable Ginibre ensemble apart from the very recent upper bounds given in [7] and [45]. As a key tool, we develop a new systematic decomposition of general observables in random matrix theory that governs the size of products of resolvents with deterministic matrices in between."}],"file_date_updated":"2025-06-24T13:14:21Z","type":"journal_article","month":"08","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","call_identifier":"H2020"}],"external_id":{"isi":["001325502400001"]},"title":"Optimal lower bound on eigenvector overlaps for non-Hermitian random matrices","article_processing_charge":"Yes (via OA deal)","date_created":"2024-05-26T22:00:57Z","oa_version":"Published Version","doi":"10.1016/j.jfa.2024.110495","department":[{"_id":"LaEr"}],"publication":"Journal of Functional Analysis","status":"public","citation":{"short":"G. Cipolloni, L. Erdös, S.J. Henheik, D.J. Schröder, Journal of Functional Analysis 287 (2024).","ista":"Cipolloni G, Erdös L, Henheik SJ, Schröder DJ. 2024. Optimal lower bound on eigenvector overlaps for non-Hermitian random matrices. Journal of Functional Analysis. 287(4), 110495.","chicago":"Cipolloni, Giorgio, László Erdös, Sven Joscha Henheik, and Dominik J Schröder. “Optimal Lower Bound on Eigenvector Overlaps for Non-Hermitian Random Matrices.” <i>Journal of Functional Analysis</i>. Elsevier, 2024. <a href=\"https://doi.org/10.1016/j.jfa.2024.110495\">https://doi.org/10.1016/j.jfa.2024.110495</a>.","ama":"Cipolloni G, Erdös L, Henheik SJ, Schröder DJ. Optimal lower bound on eigenvector overlaps for non-Hermitian random matrices. <i>Journal of Functional Analysis</i>. 2024;287(4). doi:<a href=\"https://doi.org/10.1016/j.jfa.2024.110495\">10.1016/j.jfa.2024.110495</a>","mla":"Cipolloni, Giorgio, et al. “Optimal Lower Bound on Eigenvector Overlaps for Non-Hermitian Random Matrices.” <i>Journal of Functional Analysis</i>, vol. 287, no. 4, 110495, Elsevier, 2024, doi:<a href=\"https://doi.org/10.1016/j.jfa.2024.110495\">10.1016/j.jfa.2024.110495</a>.","apa":"Cipolloni, G., Erdös, L., Henheik, S. J., &#38; Schröder, D. J. (2024). Optimal lower bound on eigenvector overlaps for non-Hermitian random matrices. <i>Journal of Functional Analysis</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jfa.2024.110495\">https://doi.org/10.1016/j.jfa.2024.110495</a>","ieee":"G. Cipolloni, L. Erdös, S. J. Henheik, and D. J. Schröder, “Optimal lower bound on eigenvector overlaps for non-Hermitian random matrices,” <i>Journal of Functional Analysis</i>, vol. 287, no. 4. Elsevier, 2024."},"OA_type":"hybrid","ddc":["510"],"article_number":"110495","has_accepted_license":"1","ec_funded":1,"scopus_import":"1","publisher":"Elsevier","file":[{"file_id":"19891","relation":"main_file","file_name":"2025_JourFunctionalAnalysis_Cipolloni.pdf","creator":"dernst","date_created":"2025-06-24T13:14:21Z","success":1,"access_level":"open_access","date_updated":"2025-06-24T13:14:21Z","content_type":"application/pdf","file_size":1374854,"checksum":"07d3f73e0c56e68eb110851842c22ee0"}],"date_updated":"2026-04-07T12:37:11Z","year":"2024","author":[{"first_name":"Giorgio","last_name":"Cipolloni","full_name":"Cipolloni, Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992"},{"full_name":"Erdös, László","last_name":"Erdös","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603"},{"full_name":"Henheik, Sven Joscha","last_name":"Henheik","first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","orcid":"0000-0003-1106-327X"},{"full_name":"Schröder, Dominik J","last_name":"Schröder","first_name":"Dominik J","orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87"}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"quality_controlled":"1","article_type":"original","oa":1,"volume":287,"issue":"4","day":"15","OA_place":"publisher","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345"},{"language":[{"iso":"eng"}],"publication_status":"draft","_id":"19545","related_material":{"record":[{"status":"public","id":"19540","relation":"dissertation_contains"}]},"date_published":"2024-12-17T00:00:00Z","external_id":{"arxiv":["2309.05488"]},"project":[{"call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"arxiv":1,"type":"preprint","month":"12","abstract":[{"lang":"eng","text":"We prove the Eigenstate Thermalisation Hypothesis for Wigner matrices\r\nuniformly in the entire spectrum, in particular near the spectral edges, with a\r\nbound on the fluctuation that is optimal for any observable. This complements\r\nearlier works of Cipolloni et. al. (Comm. Math. Phys. 388, 2021; Forum Math.,\r\nSigma 10, 2022) and Benigni et. al. (Comm. Math. Phys. 391, 2022; arXiv:\r\n2303.11142) that were restricted either to the bulk of the spectrum or to\r\nspecial observables. As a main ingredient, we prove a new multi-resolvent local\r\nlaw that optimally accounts for the edge scaling."}],"acknowledgement":"Supported by ERC Advanced Grant “RMTBeyond” No. 101020331.","corr_author":"1","department":[{"_id":"LaEr"}],"doi":"10.48550/arXiv.2309.05488","date_created":"2025-04-11T08:19:22Z","oa_version":"Preprint","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2309.05488","open_access":"1"}],"article_processing_charge":"No","title":"Eigenstate thermalisation at the edge for Wigner matrices","ec_funded":1,"citation":{"mla":"Cipolloni, Giorgio, et al. “Eigenstate Thermalisation at the Edge for Wigner Matrices.” <i>ArXiv</i>, doi:<a href=\"https://doi.org/10.48550/arXiv.2309.05488\">10.48550/arXiv.2309.05488</a>.","apa":"Cipolloni, G., Erdös, L., &#38; Henheik, S. J. (n.d.). Eigenstate thermalisation at the edge for Wigner matrices. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2309.05488\">https://doi.org/10.48550/arXiv.2309.05488</a>","ama":"Cipolloni G, Erdös L, Henheik SJ. Eigenstate thermalisation at the edge for Wigner matrices. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2309.05488\">10.48550/arXiv.2309.05488</a>","ieee":"G. Cipolloni, L. Erdös, and S. J. Henheik, “Eigenstate thermalisation at the edge for Wigner matrices,” <i>arXiv</i>. .","short":"G. Cipolloni, L. Erdös, S.J. Henheik, ArXiv (n.d.).","chicago":"Cipolloni, Giorgio, László Erdös, and Sven Joscha Henheik. “Eigenstate Thermalisation at the Edge for Wigner Matrices.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2309.05488\">https://doi.org/10.48550/arXiv.2309.05488</a>.","ista":"Cipolloni G, Erdös L, Henheik SJ. Eigenstate thermalisation at the edge for Wigner matrices. arXiv, <a href=\"https://doi.org/10.48550/arXiv.2309.05488\">10.48550/arXiv.2309.05488</a>."},"status":"public","publication":"arXiv","author":[{"orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","last_name":"Cipolloni","first_name":"Giorgio","full_name":"Cipolloni, Giorgio"},{"orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","last_name":"Erdös","full_name":"Erdös, László"},{"first_name":"Sven Joscha","last_name":"Henheik","full_name":"Henheik, Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","orcid":"0000-0003-1106-327X"}],"year":"2024","date_updated":"2026-04-07T12:37:11Z","oa":1,"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","OA_place":"repository","day":"17"},{"corr_author":"1","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"abstract":[{"lang":"eng","text":"We introduce a notion of a \\emph{local gap} for interacting many-body quantum lattice systems and prove the validity of response theory and Kubo's formula for localized perturbations in such settings.\r\nOn a high level, our result shows that the usual spectral gap condition, concerning the system as a whole, is not a necessary condition for understanding local properties of the system.\r\nMore precisely, we say that an equilibrium state ρ0 of a Hamiltonian H0 is locally gapped in Λgap⊂Λ, whenever the Liouvillian −i[H0,⋅] is almost invertible on local observables supported in Λgap when tested in ρ0.\r\nTo put this into context, we provide other alternative notions of a local gap and discuss their relations.\r\nThe validity of response theory is based on the construction of \\emph{non-equilibrium almost stationary states} (NEASSs).\r\nBy controlling locality properties of the NEASS construction, we show that response theory holds to any order, whenever the perturbation \\(\\epsilon V\\) acts in a region which is further than |logϵ| away from the non-gapped region Λ∖Λgap."}],"type":"preprint","month":"10","arxiv":1,"external_id":{"arxiv":["2410.10809"]},"oa":1,"title":"Response theory for locally gapped systems","article_processing_charge":"No","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2410.10809","open_access":"1"}],"doi":"10.48550/arXiv.2410.10809","date_created":"2025-04-11T11:54:56Z","oa_version":"Preprint","day":"14","department":[{"_id":"LaEr"}],"OA_place":"repository","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","publication_status":"draft","status":"public","publication":"arXiv","citation":{"ista":"Henheik SJ, Wessel T. Response theory for locally gapped systems. arXiv, <a href=\"https://doi.org/10.48550/arXiv.2410.10809\">10.48550/arXiv.2410.10809</a>.","chicago":"Henheik, Sven Joscha, and Tom Wessel. “Response Theory for Locally Gapped Systems.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2410.10809\">https://doi.org/10.48550/arXiv.2410.10809</a>.","short":"S.J. Henheik, T. Wessel, ArXiv (n.d.).","apa":"Henheik, S. J., &#38; Wessel, T. (n.d.). Response theory for locally gapped systems. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2410.10809\">https://doi.org/10.48550/arXiv.2410.10809</a>","ama":"Henheik SJ, Wessel T. Response theory for locally gapped systems. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2410.10809\">10.48550/arXiv.2410.10809</a>","ieee":"S. J. Henheik and T. Wessel, “Response theory for locally gapped systems,” <i>arXiv</i>. .","mla":"Henheik, Sven Joscha, and Tom Wessel. “Response Theory for Locally Gapped Systems.” <i>ArXiv</i>, doi:<a href=\"https://doi.org/10.48550/arXiv.2410.10809\">10.48550/arXiv.2410.10809</a>."},"language":[{"iso":"eng"}],"date_updated":"2026-04-07T12:37:11Z","date_published":"2024-10-14T00:00:00Z","related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"19540"}]},"_id":"19551","year":"2024","author":[{"last_name":"Henheik","first_name":"Sven Joscha","full_name":"Henheik, Sven Joscha","orcid":"0000-0003-1106-327X","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb"},{"full_name":"Wessel, Tom","last_name":"Wessel","first_name":"Tom"}]},{"day":"21","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","department":[{"_id":"LaEr"},{"_id":"RoSe"}],"OA_place":"repository","title":"Multi-band superconductors have enhanced critical temperatures","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2409.17297","open_access":"1"}],"article_processing_charge":"No","oa_version":"Preprint","doi":"10.48550/arXiv.2409.17297","date_created":"2025-04-11T11:43:58Z","abstract":[{"lang":"eng","text":"We introduce a multi-band BCS free energy functional and prove that for a\r\nmulti-band superconductor the effect of inter-band coupling can only increase\r\nthe critical temperature, irrespective of its attractive or repulsive nature\r\nand its strength. Further, for weak coupling and weaker inter-band coupling, we\r\nprove that the dependence of the increase in critical temperature on the\r\ninter-band coupling is (1) linear, if there are two or more equally strongly\r\nsuperconducting bands, or (2) quadratic, if there is only one dominating band."}],"month":"10","arxiv":1,"type":"preprint","external_id":{"arxiv":["2409.17297"]},"oa":1,"corr_author":"1","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"19540"}]},"_id":"19550","year":"2024","author":[{"orcid":"0000-0003-1106-327X","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","last_name":"Henheik","first_name":"Sven Joscha","full_name":"Henheik, Sven Joscha"},{"last_name":"Langmann","first_name":"Edwin","full_name":"Langmann, Edwin"},{"full_name":"Lauritsen, Asbjørn Bækgaard","first_name":"Asbjørn Bækgaard","last_name":"Lauritsen","orcid":"0000-0003-4476-2288","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1"}],"date_updated":"2026-04-07T12:37:11Z","date_published":"2024-10-21T00:00:00Z","language":[{"iso":"eng"}],"publication_status":"draft","publication":"arXiv","status":"public","citation":{"apa":"Henheik, S. J., Langmann, E., &#38; Lauritsen, A. B. (n.d.). Multi-band superconductors have enhanced critical temperatures. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2409.17297\">https://doi.org/10.48550/arXiv.2409.17297</a>","ama":"Henheik SJ, Langmann E, Lauritsen AB. Multi-band superconductors have enhanced critical temperatures. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2409.17297\">10.48550/arXiv.2409.17297</a>","ieee":"S. J. Henheik, E. Langmann, and A. B. Lauritsen, “Multi-band superconductors have enhanced critical temperatures,” <i>arXiv</i>. .","mla":"Henheik, Sven Joscha, et al. “Multi-Band Superconductors Have Enhanced Critical Temperatures.” <i>ArXiv</i>, doi:<a href=\"https://doi.org/10.48550/arXiv.2409.17297\">10.48550/arXiv.2409.17297</a>.","ista":"Henheik SJ, Langmann E, Lauritsen AB. Multi-band superconductors have enhanced critical temperatures. arXiv, <a href=\"https://doi.org/10.48550/arXiv.2409.17297\">10.48550/arXiv.2409.17297</a>.","short":"S.J. Henheik, E. Langmann, A.B. Lauritsen, ArXiv (n.d.).","chicago":"Henheik, Sven Joscha, Edwin Langmann, and Asbjørn Bækgaard Lauritsen. “Multi-Band Superconductors Have Enhanced Critical Temperatures.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2409.17297\">https://doi.org/10.48550/arXiv.2409.17297</a>."}},{"language":[{"iso":"eng"}],"publication_status":"draft","related_material":{"record":[{"status":"public","relation":"later_version","id":"20322"},{"status":"public","relation":"dissertation_contains","id":"20575"},{"id":"19540","relation":"dissertation_contains","status":"public"}]},"_id":"19547","date_published":"2024-11-03T00:00:00Z","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020"}],"external_id":{"arxiv":["2410.06813"]},"abstract":[{"text":"For correlated real symmetric or complex Hermitian random matrices, we prove\r\nthat the local eigenvalue statistics at any cusp singularity are universal.\r\nSince the density of states typically exhibits only square root edge or cubic\r\nroot cusp singularities, our result completes the proof of the\r\nWigner-Dyson-Mehta universality conjecture in all spectral regimes for a very\r\ngeneral class of random matrices. Previously only the bulk and the edge\r\nuniversality were established in this generality [arXiv:1804.07744], while cusp\r\nuniversality was proven only for Wigner-type matrices with independent entries\r\n[arXiv:1809.03971, arXiv:1811.04055]. As our main technical input, we prove an\r\noptimal local law at the cusp using the Zigzag strategy, a recursive tandem of\r\nthe characteristic flow method and a Green function comparison argument.\r\nMoreover, our proof of the optimal local law holds uniformly in the spectrum,\r\nthus also re-establishing universality of the local eigenvalue statistics in\r\nthe previously studied bulk [arXiv:1705.10661] and edge [arXiv:1804.07744]\r\nregimes.","lang":"eng"}],"type":"preprint","arxiv":1,"month":"11","corr_author":"1","acknowledgement":"Supported by the ERC Advanced Grant \"RMTBeyond\"\r\nNo. 101020331.","department":[{"_id":"LaEr"}],"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2410.06813","open_access":"1"}],"article_processing_charge":"No","doi":"10.48550/arXiv.2410.06813","oa_version":"Preprint","date_created":"2025-04-11T08:48:21Z","title":"Cusp universality for correlated random matrices","ec_funded":1,"citation":{"ieee":"L. Erdös, S. J. Henheik, and V. Riabov, “Cusp universality for correlated random matrices,” <i>arXiv</i>. .","apa":"Erdös, L., Henheik, S. J., &#38; Riabov, V. (n.d.). Cusp universality for correlated random matrices. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2410.06813\">https://doi.org/10.48550/arXiv.2410.06813</a>","mla":"Erdös, László, et al. “Cusp Universality for Correlated Random Matrices.” <i>ArXiv</i>, doi:<a href=\"https://doi.org/10.48550/arXiv.2410.06813\">10.48550/arXiv.2410.06813</a>.","ama":"Erdös L, Henheik SJ, Riabov V. Cusp universality for correlated random matrices. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2410.06813\">10.48550/arXiv.2410.06813</a>","ista":"Erdös L, Henheik SJ, Riabov V. Cusp universality for correlated random matrices. arXiv, <a href=\"https://doi.org/10.48550/arXiv.2410.06813\">10.48550/arXiv.2410.06813</a>.","short":"L. Erdös, S.J. Henheik, V. Riabov, ArXiv (n.d.).","chicago":"Erdös, László, Sven Joscha Henheik, and Volodymyr Riabov. “Cusp Universality for Correlated Random Matrices.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2410.06813\">https://doi.org/10.48550/arXiv.2410.06813</a>."},"publication":"arXiv","status":"public","year":"2024","author":[{"full_name":"Erdös, László","first_name":"László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603"},{"id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","orcid":"0000-0003-1106-327X","first_name":"Sven Joscha","last_name":"Henheik","full_name":"Henheik, Sven Joscha"},{"id":"1949f904-edfb-11eb-afb5-e2dfddabb93b","full_name":"Riabov, Volodymyr","last_name":"Riabov","first_name":"Volodymyr"}],"date_updated":"2026-04-07T12:37:11Z","oa":1,"OA_place":"repository","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","day":"03"},{"author":[{"id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","orcid":"0000-0003-1106-327X","full_name":"Henheik, Sven Joscha","last_name":"Henheik","first_name":"Sven Joscha"},{"id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1","orcid":"0000-0003-4476-2288","last_name":"Lauritsen","first_name":"Asbjørn Bækgaard","full_name":"Lauritsen, Asbjørn Bækgaard"},{"id":"5DA90512-D80F-11E9-8994-2E2EE6697425","orcid":"0000-0002-9071-5880","last_name":"Roos","first_name":"Barbara","full_name":"Roos, Barbara"}],"year":"2024","date_updated":"2026-04-07T13:01:40Z","file":[{"content_type":"application/pdf","file_size":503910,"checksum":"2b053a4223b4db14b90520999ec56054","date_updated":"2025-01-09T07:56:28Z","access_level":"open_access","date_created":"2025-01-09T07:56:28Z","success":1,"file_name":"2024_ReviewsmathPhysics_Henheik.pdf","creator":"dernst","file_id":"18786","relation":"main_file"}],"publisher":"World Scientific Publishing","has_accepted_license":"1","ec_funded":1,"scopus_import":"1","publication":"Reviews in Mathematical Physics","status":"public","article_number":"2360005 ","ddc":["510"],"OA_type":"hybrid","citation":{"chicago":"Henheik, Sven Joscha, Asbjørn Bækgaard Lauritsen, and Barbara Roos. “Universality in Low-Dimensional BCS Theory.” <i>Reviews in Mathematical Physics</i>. World Scientific Publishing, 2024. <a href=\"https://doi.org/10.1142/s0129055x2360005x\">https://doi.org/10.1142/s0129055x2360005x</a>.","short":"S.J. Henheik, A.B. Lauritsen, B. Roos, Reviews in Mathematical Physics 36 (2024).","ista":"Henheik SJ, Lauritsen AB, Roos B. 2024. Universality in low-dimensional BCS theory. Reviews in Mathematical Physics. 36(9), 2360005.","apa":"Henheik, S. J., Lauritsen, A. B., &#38; Roos, B. (2024). Universality in low-dimensional BCS theory. <i>Reviews in Mathematical Physics</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/s0129055x2360005x\">https://doi.org/10.1142/s0129055x2360005x</a>","mla":"Henheik, Sven Joscha, et al. “Universality in Low-Dimensional BCS Theory.” <i>Reviews in Mathematical Physics</i>, vol. 36, no. 9, 2360005, World Scientific Publishing, 2024, doi:<a href=\"https://doi.org/10.1142/s0129055x2360005x\">10.1142/s0129055x2360005x</a>.","ieee":"S. J. Henheik, A. B. Lauritsen, and B. Roos, “Universality in low-dimensional BCS theory,” <i>Reviews in Mathematical Physics</i>, vol. 36, no. 9. World Scientific Publishing, 2024.","ama":"Henheik SJ, Lauritsen AB, Roos B. Universality in low-dimensional BCS theory. <i>Reviews in Mathematical Physics</i>. 2024;36(9). doi:<a href=\"https://doi.org/10.1142/s0129055x2360005x\">10.1142/s0129055x2360005x</a>"},"day":"01","OA_place":"publisher","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","volume":36,"issue":"9","article_type":"original","quality_controlled":"1","oa":1,"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"isi":1,"_id":"14542","related_material":{"record":[{"id":"19540","relation":"dissertation_contains","status":"public"},{"id":"18135","relation":"dissertation_contains","status":"public"}]},"date_published":"2024-10-01T00:00:00Z","language":[{"iso":"eng"}],"intvolume":"        36","publication_status":"published","department":[{"_id":"GradSch"},{"_id":"LaEr"},{"_id":"RoSe"}],"title":"Universality in low-dimensional BCS theory","oa_version":"Published Version","doi":"10.1142/s0129055x2360005x","date_created":"2023-11-15T23:48:14Z","article_processing_charge":"Yes (in subscription journal)","arxiv":1,"type":"journal_article","file_date_updated":"2025-01-09T07:56:28Z","month":"10","abstract":[{"text":"It is a remarkable property of BCS theory that the ratio of the energy gap at zero temperature Ξ\r\n and the critical temperature Tc is (approximately) given by a universal constant, independent of the microscopic details of the fermionic interaction. This universality has rigorously been proven quite recently in three spatial dimensions and three different limiting regimes: weak coupling, low density and high density. The goal of this short note is to extend the universal behavior to lower dimensions d=1,2 and give an exemplary proof in the weak coupling limit.","lang":"eng"}],"external_id":{"arxiv":["2301.05621"],"isi":["001099640300002"]},"project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"},{"name":"Mathematical Challenges in BCS Theory of Superconductivity","grant_number":"I06427","_id":"bda63fe5-d553-11ed-ba76-a16e3d2f256b"}],"publication_identifier":{"eissn":["1793-6659"],"issn":["0129-055X"]},"acknowledgement":"We thank Robert Seiringer for comments on the paper. J. H. gratefully acknowledges  partial  financial  support  by  the  ERC  Advanced  Grant  “RMTBeyond”No. 101020331.This research was funded in part by the Austrian Science Fund (FWF) grantnumber I6427.","corr_author":"1"},{"has_accepted_license":"1","ec_funded":1,"publisher":"Institute of Science and Technology Austria","file":[{"content_type":"application/pdf","file_size":2783027,"checksum":"fb16d86e1f2753dc3a9e14d2bdfd84cd","date_updated":"2024-06-26T12:44:53Z","access_level":"open_access","date_created":"2024-06-26T12:39:36Z","file_name":"ISTA_Thesis_JReker.pdf","creator":"jreker","file_id":"17176","relation":"main_file"},{"date_created":"2024-06-26T12:39:42Z","access_level":"closed","date_updated":"2024-06-26T12:44:53Z","file_size":3054878,"checksum":"cb1e54009d47c1dcf5b866c4566fa27f","content_type":"application/zip","relation":"source_file","file_id":"17177","creator":"jreker","file_name":"ISTA_Thesis_JReker_SourceFiles.zip"}],"ddc":["519"],"citation":{"apa":"Reker, J. (2024). <i>Central limit theorems for random matrices: From resolvents to free probability</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/at:ista:17164\">https://doi.org/10.15479/at:ista:17164</a>","ama":"Reker J. Central limit theorems for random matrices: From resolvents to free probability. 2024. doi:<a href=\"https://doi.org/10.15479/at:ista:17164\">10.15479/at:ista:17164</a>","mla":"Reker, Jana. <i>Central Limit Theorems for Random Matrices: From Resolvents to Free Probability</i>. Institute of Science and Technology Austria, 2024, doi:<a href=\"https://doi.org/10.15479/at:ista:17164\">10.15479/at:ista:17164</a>.","ieee":"J. Reker, “Central limit theorems for random matrices: From resolvents to free probability,” Institute of Science and Technology Austria, 2024.","short":"J. Reker, Central Limit Theorems for Random Matrices: From Resolvents to Free Probability, Institute of Science and Technology Austria, 2024.","ista":"Reker J. 2024. Central limit theorems for random matrices: From resolvents to free probability. Institute of Science and Technology Austria.","chicago":"Reker, Jana. “Central Limit Theorems for Random Matrices: From Resolvents to Free Probability.” Institute of Science and Technology Austria, 2024. <a href=\"https://doi.org/10.15479/at:ista:17164\">https://doi.org/10.15479/at:ista:17164</a>."},"page":"206","status":"public","year":"2024","author":[{"id":"e796e4f9-dc8d-11ea-abe3-97e26a0323e9","first_name":"Jana","last_name":"Reker","full_name":"Reker, Jana"}],"date_updated":"2026-04-07T13:02:13Z","oa":1,"tmp":{"image":"/images/cc_by_nc_sa.png","short":"CC BY-NC-SA (4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode","name":"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)"},"user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","OA_place":"publisher","alternative_title":["ISTA Thesis"],"day":"26","supervisor":[{"orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","first_name":"László","last_name":"Erdös"}],"language":[{"iso":"eng"}],"publication_status":"published","keyword":["Random Matrices","Spectrum","Central Limit Theorem","Resolvent","Free Probability"],"_id":"17164","related_material":{"record":[{"status":"public","relation":"part_of_dissertation","id":"17173"},{"id":"11135","relation":"part_of_dissertation","status":"public"},{"status":"public","relation":"part_of_dissertation","id":"17047"},{"status":"public","relation":"part_of_dissertation","id":"17154"},{"status":"public","id":"17174","relation":"part_of_dissertation"}]},"date_published":"2024-06-26T00:00:00Z","project":[{"call_identifier":"H2020","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"abstract":[{"lang":"eng","text":"This thesis is structured into two parts. In the first part, we consider the random\r\nvariable X := Tr(f1(W)A1 . . . fk(W)Ak) where W is an N × N Hermitian Wigner matrix, k ∈ N, and we choose (possibly N-dependent) regular functions f1, . . . , fk as well as\r\nbounded deterministic matrices A1, . . . , Ak. In this context, we prove a functional central\r\nlimit theorem on macroscopic and mesoscopic scales, showing that the fluctuations of X\r\naround its expectation are Gaussian and that the limiting covariance structure is given\r\nby a deterministic recursion. We further give explicit error bounds in terms of the scaling\r\nof f1, . . . , fk and the number of traceless matrices among A1, . . . , Ak, thus extending\r\nthe results of Cipolloni, Erdős and Schröder [40] to products of arbitrary length k ≥ 2.\r\nAnalyzing the underlying combinatorics leads to a non-recursive formula for the variance\r\nof X as well as the covariance of X and Y := Tr(fk+1(W)Ak+1 . . . fk+ℓ(W)Ak+ℓ) of similar\r\nbuild. When restricted to polynomials, these formulas reproduce recent results of Male,\r\nMingo, Peché, and Speicher [107], showing that the underlying combinatorics of noncrossing partitions and annular non-crossing permutations continue to stay valid beyond\r\nthe setting of second-order free probability theory. As an application, we consider the\r\nfluctuation of Tr(eitW A1e\r\n−itW A2)/N around its thermal value Tr(A1) Tr(A2)/N2 when t\r\nis large and give an explicit formula for the variance.\r\nThe second part of the thesis collects three smaller projects focusing on different random\r\nmatrix models. In the first project, we show that a class of weakly perturbed Hamiltonians\r\nof the form Hλ = H0 + λW, where W is a Wigner matrix, exhibits prethermalization.\r\nThat is, the time evolution generated by Hλ relaxes to its ultimate thermal state via an\r\nintermediate prethermal state with a lifetime of order λ\r\n−2\r\n. As the main result, we obtain\r\na general relaxation formula, expressing the perturbed dynamics via the unperturbed\r\ndynamics and the ultimate thermal state. The proof relies on a two-resolvent global law\r\nfor the deformed Wigner matrix Hλ.\r\nThe second project focuses on correlated random matrices, more precisely on a correlated N × N Hermitian random matrix with a polynomially decaying metric correlation\r\nstructure. A trivial a priori bound shows that the operator norm of this model is stochastically dominated by √\r\nN. However, by calculating the trace of the moments of the matrix\r\nand using the summable decay of the cumulants, the norm estimate can be improved to a\r\nbound of order one.\r\nIn the third project, we consider a multiplicative perturbation of the form UA(t) where U\r\nis a unitary random matrix and A = diag(t, 1, ..., 1). This so-called UA model was\r\nfirst introduced by Fyodorov [73] for its applications in scattering theory. We give a\r\ngeneral description of the eigenvalue trajectories obtained by varying the parameter t and\r\nintroduce a flow of deterministic domains that separates the outlier resulting from the\r\nrank-one perturbation from the typical eigenvalues for all sub-critical timescales. The\r\nresults are obtained under generic assumptions on U that hold for various unitary random\r\nmatrices, including the circular unitary ensemble (CUE) in the original formulation of\r\nthe model."}],"type":"dissertation","month":"06","file_date_updated":"2024-06-26T12:44:53Z","corr_author":"1","publication_identifier":{"issn":["2663-337X"]},"department":[{"_id":"GradSch"},{"_id":"LaEr"}],"degree_awarded":"PhD","article_processing_charge":"No","doi":"10.15479/at:ista:17164","date_created":"2024-06-24T11:23:29Z","oa_version":"Published Version","title":"Central limit theorems for random matrices: From resolvents to free probability"},{"volume":27,"issue":"3","day":"20","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"quality_controlled":"1","article_type":"original","oa":1,"date_updated":"2026-04-07T13:02:12Z","year":"2024","author":[{"id":"e796e4f9-dc8d-11ea-abe3-97e26a0323e9","last_name":"Reker","first_name":"Jana","full_name":"Reker, Jana"}],"status":"public","publication":"Mathematical Physics, Analysis and Geometry","ddc":["519"],"citation":{"short":"J. Reker, Mathematical Physics, Analysis and Geometry 27 (2024).","ista":"Reker J. 2024. Fluctuation moments for regular functions of Wigner Matrices. Mathematical Physics, Analysis and Geometry. 27(3), 10.","chicago":"Reker, Jana. “Fluctuation Moments for Regular Functions of Wigner Matrices.” <i>Mathematical Physics, Analysis and Geometry</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s11040-024-09483-y\">https://doi.org/10.1007/s11040-024-09483-y</a>.","ama":"Reker J. Fluctuation moments for regular functions of Wigner Matrices. <i>Mathematical Physics, Analysis and Geometry</i>. 2024;27(3). doi:<a href=\"https://doi.org/10.1007/s11040-024-09483-y\">10.1007/s11040-024-09483-y</a>","mla":"Reker, Jana. “Fluctuation Moments for Regular Functions of Wigner Matrices.” <i>Mathematical Physics, Analysis and Geometry</i>, vol. 27, no. 3, 10, Springer Nature, 2024, doi:<a href=\"https://doi.org/10.1007/s11040-024-09483-y\">10.1007/s11040-024-09483-y</a>.","apa":"Reker, J. (2024). Fluctuation moments for regular functions of Wigner Matrices. <i>Mathematical Physics, Analysis and Geometry</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s11040-024-09483-y\">https://doi.org/10.1007/s11040-024-09483-y</a>","ieee":"J. Reker, “Fluctuation moments for regular functions of Wigner Matrices,” <i>Mathematical Physics, Analysis and Geometry</i>, vol. 27, no. 3. Springer Nature, 2024."},"article_number":"10","scopus_import":"1","has_accepted_license":"1","ec_funded":1,"file":[{"date_updated":"2024-06-26T11:26:42Z","access_level":"open_access","success":1,"date_created":"2024-06-26T11:26:42Z","content_type":"application/pdf","file_size":1327596,"checksum":"7d04318d66f765621bdcb648378d458e","file_name":"2024_MathPhysAnaGeo_Reker.pdf","creator":"cchlebak","file_id":"17175","relation":"main_file"}],"publisher":"Springer Nature","title":"Fluctuation moments for regular functions of Wigner Matrices","article_processing_charge":"Yes (via OA deal)","doi":"10.1007/s11040-024-09483-y","oa_version":"Published Version","date_created":"2024-06-21T09:31:17Z","department":[{"_id":"LaEr"}],"publication_identifier":{"eissn":["1572-9656"],"issn":["1385-0172"]},"abstract":[{"text":"We compute the deterministic approximation for mixed fluctuation moments of products of deterministic matrices and general Sobolev functions of Wigner matrices. Restricting to polynomials, our formulas reproduce recent results of Male et al. (Random Matrices Theory Appl. 11(2):2250015, 2022), showing that the underlying combinatorics of non-crossing partitions and annular non-crossing permutations continue to stay valid beyond the setting of second-order free probability theory. The formulas obtained further characterize the variance in the functional central limit theorem given in the recent companion paper (Reker in Preprint, arXiv:2204.03419, 2023). and thus allow identifying the fluctuation around the thermal value in certain thermalization problems.","lang":"eng"}],"type":"journal_article","arxiv":1,"file_date_updated":"2024-06-26T11:26:42Z","month":"06","project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"},{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"}],"external_id":{"arxiv":["2307.11029"],"isi":["001251464300001"]},"date_published":"2024-06-20T00:00:00Z","isi":1,"_id":"17154","related_material":{"record":[{"id":"17164","relation":"dissertation_contains","status":"public"}]},"publication_status":"published","intvolume":"        27","language":[{"iso":"eng"}]},{"publication_status":"published","intvolume":"        13","language":[{"iso":"eng"}],"date_published":"2024-04-01T00:00:00Z","_id":"17047","related_material":{"record":[{"relation":"dissertation_contains","id":"17164","status":"public"}]},"isi":1,"corr_author":"1","publication_identifier":{"eissn":["2010-3271"],"issn":["2010-3263"]},"project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020"}],"external_id":{"arxiv":["2212.14638"],"isi":["001229295200002"]},"abstract":[{"text":"We provide a dynamical study of a model of multiplicative perturbation of a unitary matrix introduced by Fyodorov. In particular, we identify a flow of deterministic domains that bound the spectrum with high probability, separating the outlier from the typical eigenvalues at all sub-critical timescales. These results are obtained under generic assumptions on U that hold for a variety of unitary random matrix models.","lang":"eng"}],"arxiv":1,"month":"04","type":"journal_article","article_processing_charge":"No","main_file_link":[{"open_access":"1","url":" https://doi.org/10.48550/arXiv.2212.14638"}],"date_created":"2024-05-23T08:31:57Z","doi":"10.1142/s2010326324500072","oa_version":"Preprint","title":"Dynamics of a rank-one multiplicative perturbation of a unitary matrix","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"article_number":"2450007","OA_type":"green","citation":{"ista":"Dubach G, Reker J. 2024. Dynamics of a rank-one multiplicative perturbation of a unitary matrix. Random Matrices: Theory and Applications. 13(2), 2450007.","chicago":"Dubach, Guillaume, and Jana Reker. “Dynamics of a Rank-One Multiplicative Perturbation of a Unitary Matrix.” <i>Random Matrices: Theory and Applications</i>. World Scientific Publishing, 2024. <a href=\"https://doi.org/10.1142/s2010326324500072\">https://doi.org/10.1142/s2010326324500072</a>.","short":"G. Dubach, J. Reker, Random Matrices: Theory and Applications 13 (2024).","ama":"Dubach G, Reker J. Dynamics of a rank-one multiplicative perturbation of a unitary matrix. <i>Random Matrices: Theory and Applications</i>. 2024;13(2). doi:<a href=\"https://doi.org/10.1142/s2010326324500072\">10.1142/s2010326324500072</a>","apa":"Dubach, G., &#38; Reker, J. (2024). Dynamics of a rank-one multiplicative perturbation of a unitary matrix. <i>Random Matrices: Theory and Applications</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/s2010326324500072\">https://doi.org/10.1142/s2010326324500072</a>","mla":"Dubach, Guillaume, and Jana Reker. “Dynamics of a Rank-One Multiplicative Perturbation of a Unitary Matrix.” <i>Random Matrices: Theory and Applications</i>, vol. 13, no. 2, 2450007, World Scientific Publishing, 2024, doi:<a href=\"https://doi.org/10.1142/s2010326324500072\">10.1142/s2010326324500072</a>.","ieee":"G. Dubach and J. Reker, “Dynamics of a rank-one multiplicative perturbation of a unitary matrix,” <i>Random Matrices: Theory and Applications</i>, vol. 13, no. 2. World Scientific Publishing, 2024."},"status":"public","publication":"Random Matrices: Theory and Applications","ec_funded":1,"scopus_import":"1","publisher":"World Scientific Publishing","date_updated":"2026-04-07T13:02:12Z","year":"2024","author":[{"full_name":"Dubach, Guillaume","first_name":"Guillaume","last_name":"Dubach","orcid":"0000-0001-6892-8137","id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E"},{"first_name":"Jana","last_name":"Reker","full_name":"Reker, Jana","id":"e796e4f9-dc8d-11ea-abe3-97e26a0323e9"}],"oa":1,"quality_controlled":"1","article_type":"original","issue":"2","volume":13,"OA_place":"repository","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","day":"01"},{"language":[{"iso":"eng"}],"intvolume":"       185","publication_status":"published","_id":"11741","isi":1,"date_published":"2023-04-01T00:00:00Z","external_id":{"isi":["000830344500001"],"arxiv":["2106.10200"]},"type":"journal_article","arxiv":1,"file_date_updated":"2023-08-14T12:47:32Z","month":"04","abstract":[{"lang":"eng","text":"Following E. Wigner’s original vision, we prove that sampling the eigenvalue gaps within the bulk spectrum of a fixed (deformed) Wigner matrix H yields the celebrated Wigner-Dyson-Mehta universal statistics with high probability. Similarly, we prove universality for a monoparametric family of deformed Wigner matrices H+xA with a deterministic Hermitian matrix A and a fixed Wigner matrix H, just using the randomness of a single scalar real random variable x. Both results constitute quenched versions of bulk universality that has so far only been proven in annealed sense with respect to the probability space of the matrix ensemble."}],"acknowledgement":"The authors are indebted to Sourav Chatterjee for forwarding the very inspiring question that Stephen Shenker originally addressed to him which initiated the current paper. They are also grateful that the authors of [23] kindly shared their preliminary numerical results in June 2021.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria).","corr_author":"1","publication_identifier":{"issn":["0178-8051"],"eissn":["1432-2064"]},"department":[{"_id":"LaEr"}],"doi":"10.1007/s00440-022-01156-7","oa_version":"Published Version","date_created":"2022-08-07T22:02:00Z","article_processing_charge":"Yes (via OA deal)","title":"Quenched universality for deformed Wigner matrices","file":[{"relation":"main_file","file_id":"14054","creator":"dernst","file_name":"2023_ProbabilityTheory_Cipolloni.pdf","checksum":"b9247827dae5544d1d19c37abe547abc","content_type":"application/pdf","file_size":782278,"date_created":"2023-08-14T12:47:32Z","success":1,"access_level":"open_access","date_updated":"2023-08-14T12:47:32Z"}],"publisher":"Springer Nature","has_accepted_license":"1","scopus_import":"1","page":"1183–1218","ddc":["510"],"citation":{"short":"G. Cipolloni, L. Erdös, D.J. Schröder, Probability Theory and Related Fields 185 (2023) 1183–1218.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Quenched Universality for Deformed Wigner Matrices.” <i>Probability Theory and Related Fields</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00440-022-01156-7\">https://doi.org/10.1007/s00440-022-01156-7</a>.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2023. Quenched universality for deformed Wigner matrices. Probability Theory and Related Fields. 185, 1183–1218.","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2023). Quenched universality for deformed Wigner matrices. <i>Probability Theory and Related Fields</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00440-022-01156-7\">https://doi.org/10.1007/s00440-022-01156-7</a>","mla":"Cipolloni, Giorgio, et al. “Quenched Universality for Deformed Wigner Matrices.” <i>Probability Theory and Related Fields</i>, vol. 185, Springer Nature, 2023, pp. 1183–1218, doi:<a href=\"https://doi.org/10.1007/s00440-022-01156-7\">10.1007/s00440-022-01156-7</a>.","ama":"Cipolloni G, Erdös L, Schröder DJ. Quenched universality for deformed Wigner matrices. <i>Probability Theory and Related Fields</i>. 2023;185:1183–1218. doi:<a href=\"https://doi.org/10.1007/s00440-022-01156-7\">10.1007/s00440-022-01156-7</a>","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Quenched universality for deformed Wigner matrices,” <i>Probability Theory and Related Fields</i>, vol. 185. Springer Nature, pp. 1183–1218, 2023."},"status":"public","publication":"Probability Theory and Related Fields","author":[{"orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio","last_name":"Cipolloni","full_name":"Cipolloni, Giorgio"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","first_name":"László","last_name":"Erdös","full_name":"Erdös, László"},{"first_name":"Dominik J","last_name":"Schröder","full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87"}],"year":"2023","date_updated":"2024-10-09T21:03:02Z","oa":1,"article_type":"original","quality_controlled":"1","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"01","volume":185}]