[{"external_id":{"arxiv":["2301.04981"],"isi":["001217139900001"]},"status":"public","article_processing_charge":"Yes (via OA deal)","department":[{"_id":"LaEr"}],"has_accepted_license":"1","isi":1,"publication":"Communications on Pure and Applied Mathematics","language":[{"iso":"eng"}],"file":[{"success":1,"content_type":"application/pdf","date_updated":"2025-01-09T09:36:41Z","file_size":566963,"creator":"dernst","access_level":"open_access","file_id":"18803","date_created":"2025-01-09T09:36:41Z","checksum":"fbcc9cc7bf274f024e4f4afc9c208f96","file_name":"2024_CommPureApplMath_Erdoes.pdf","relation":"main_file"}],"date_updated":"2025-09-08T07:25:47Z","ddc":["510"],"publisher":"Wiley","month":"09","corr_author":"1","OA_type":"hybrid","license":"https://creativecommons.org/licenses/by-nc-nd/4.0/","issue":"9","day":"01","ec_funded":1,"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","image":"/images/cc_by_nc_nd.png","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","short":"CC BY-NC-ND (4.0)"},"project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331"}],"type":"journal_article","year":"2024","page":"3785-3840","quality_controlled":"1","file_date_updated":"2025-01-09T09:36:41Z","abstract":[{"lang":"eng","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."}],"publication_status":"published","oa_version":"Published Version","title":"Wegner estimate and upper bound on the eigenvalue condition number of non-Hermitian random matrices","date_created":"2024-05-12T22:01:02Z","doi":"10.1002/cpa.22201","author":[{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","last_name":"Erdös","orcid":"0000-0001-5366-9603","first_name":"László"},{"first_name":"Hong Chang","last_name":"Ji","full_name":"Ji, Hong Chang","id":"dd216c0a-c1f9-11eb-beaf-e9ea9d2de76d"}],"OA_place":"publisher","scopus_import":"1","_id":"15378","arxiv":1,"citation":{"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>.","short":"L. Erdös, H.C. Ji, Communications on Pure and Applied Mathematics 77 (2024) 3785–3840.","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.","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."},"oa":1,"date_published":"2024-09-01T00:00:00Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","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.","intvolume":"        77","article_type":"original","volume":77,"publication_identifier":{"issn":["0010-3640"],"eissn":["1097-0312"]}},{"type":"journal_article","year":"2024","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"license":"https://creativecommons.org/licenses/by/4.0/","day":"01","issue":"13","publisher":"Oxford University Press","month":"07","corr_author":"1","file":[{"file_size":1233508,"date_updated":"2024-07-22T06:40:19Z","content_type":"application/pdf","success":1,"date_created":"2024-07-22T06:40:19Z","checksum":"f36a7dbf53f23d5833db711052e69b49","file_id":"17288","file_name":"2024_IMRN_Campbell.pdf","creator":"dernst","access_level":"open_access","relation":"main_file"}],"date_updated":"2025-09-08T08:16:32Z","ddc":["510"],"language":[{"iso":"eng"}],"article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","department":[{"_id":"LaEr"}],"isi":1,"publication":"International Mathematics Research Notices","external_id":{"isi":["001198019500001"]},"status":"public","article_type":"original","publication_identifier":{"eissn":["1687-0247"],"issn":["1073-7928"]},"volume":2024,"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.","intvolume":"      2024","citation":{"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>","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>.","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>.","short":"A.J. Campbell, S. O’Rourke, D.T. Renfrew, International Mathematics Research Notices 2024 (2024) 10189–10218.","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>","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.","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."},"date_published":"2024-07-01T00:00:00Z","oa":1,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","doi":"10.1093/imrn/rnae062","author":[{"id":"582b06a9-1f1c-11ee-b076-82ffce00dde4","full_name":"Campbell, Andrew J","last_name":"Campbell","first_name":"Andrew J"},{"full_name":"O'Rourke, Sean","last_name":"O'Rourke","first_name":"Sean"},{"last_name":"Renfrew","orcid":"0000-0003-3493-121X","first_name":"David T","id":"4845BF6A-F248-11E8-B48F-1D18A9856A87","full_name":"Renfrew, David T"}],"date_created":"2024-07-21T22:01:01Z","scopus_import":"1","_id":"17281","publication_status":"published","oa_version":"Published Version","title":"The fractional free convolution of R-diagonal elements and random polynomials under repeated differentiation","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"}],"quality_controlled":"1","file_date_updated":"2024-07-22T06:40:19Z","page":"10189-10218"},{"quality_controlled":"1","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2210.15643","open_access":"1"}],"title":"Precise asymptotics for the spectral radius of a large random matrix","oa_version":"Preprint","publication_status":"published","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."}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","arxiv":1,"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.","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.","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>","short":"G. Cipolloni, L. Erdös, Y. Xu, Journal of Mathematical Physics 65 (2024).","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>.","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>.","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>"},"date_published":"2024-06-01T00:00:00Z","oa":1,"scopus_import":"1","_id":"17375","author":[{"first_name":"Giorgio","orcid":"0000-0002-4901-7992","last_name":"Cipolloni","full_name":"Cipolloni, Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Erdös","orcid":"0000-0001-5366-9603","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László"},{"first_name":"Yuanyuan","orcid":"0000-0003-1559-1205","last_name":"Xu","full_name":"Xu, Yuanyuan","id":"7902bdb1-a2a4-11eb-a164-c9216f71aea3"}],"date_created":"2024-08-04T22:01:22Z","doi":"10.1063/5.0209705","article_type":"original","publication_identifier":{"issn":["0022-2488"]},"volume":65,"acknowledgement":"L.E. and Y.X. were supported by the ERC Advanced Grant “RMTBeyond” Grant No. 101020331.","intvolume":"        65","department":[{"_id":"LaEr"}],"isi":1,"publication":"Journal of Mathematical Physics","article_processing_charge":"No","status":"public","article_number":"063302","external_id":{"arxiv":["2210.15643"],"isi":["001252240700002"]},"date_updated":"2025-09-08T08:44:57Z","language":[{"iso":"eng"}],"day":"01","issue":"6","month":"06","corr_author":"1","publisher":"AIP Publishing","year":"2024","type":"journal_article","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"ec_funded":1},{"doi":"10.1007/s00220-024-05143-y","date_created":"2024-11-17T23:01:46Z","author":[{"orcid":"0000-0001-5366-9603","last_name":"Erdös","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László"},{"last_name":"Riabov","first_name":"Volodymyr","id":"1949f904-edfb-11eb-afb5-e2dfddabb93b","full_name":"Riabov, Volodymyr"}],"scopus_import":"1","OA_place":"publisher","_id":"18554","arxiv":1,"citation":{"ista":"Erdös L, Riabov V. 2024. Eigenstate Thermalization Hypothesis for Wigner-type matrices. Communications in Mathematical Physics. 405(12), 282.","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>.","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>.","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>","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>"},"oa":1,"date_published":"2024-12-01T00:00:00Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria).","intvolume":"       405","article_type":"original","volume":405,"publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"file_date_updated":"2024-11-18T08:15:07Z","quality_controlled":"1","abstract":[{"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.","lang":"eng"}],"pmid":1,"publication_status":"published","oa_version":"Published Version","title":"Eigenstate Thermalization Hypothesis for Wigner-type matrices","publisher":"Springer Nature","month":"12","corr_author":"1","OA_type":"hybrid","day":"01","issue":"12","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"type":"journal_article","year":"2024","article_number":"282","external_id":{"arxiv":["2403.10359"],"isi":["001348943900004"],"pmid":["39526190"]},"status":"public","article_processing_charge":"Yes (via OA deal)","isi":1,"department":[{"_id":"LaEr"}],"has_accepted_license":"1","publication":"Communications in Mathematical Physics","language":[{"iso":"eng"}],"related_material":{"record":[{"status":"public","id":"20575","relation":"dissertation_contains"}]},"ddc":["510"],"file":[{"success":1,"file_size":1426046,"date_updated":"2024-11-18T08:15:07Z","content_type":"application/pdf","relation":"main_file","access_level":"open_access","creator":"dernst","file_id":"18562","file_name":"2024_CommMathPhysics_Erdoes.pdf","checksum":"c9ae0ea195bd39b8b3a630d492fb00dc","date_created":"2024-11-18T08:15:07Z"}],"date_updated":"2026-04-07T12:32:19Z"},{"language":[{"iso":"eng"}],"related_material":{"record":[{"relation":"dissertation_contains","id":"19540","status":"public"}]},"date_updated":"2026-04-07T12:37:10Z","external_id":{"arxiv":["2402.17609"]},"status":"public","article_processing_charge":"No","department":[{"_id":"LaEr"}],"publication":"Advances in Theoretical and Mathematical Physics","ec_funded":1,"project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020"}],"type":"journal_article","year":"2024","publisher":"International Press","month":"10","corr_author":"1","OA_type":"green","day":"30","issue":"6","abstract":[{"lang":"eng","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])."}],"publication_status":"published","title":"Out-of-time-ordered correlators for Wigner matrices","oa_version":"Preprint","page":"2025-2083","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2402.17609","open_access":"1"}],"quality_controlled":"1","acknowledgement":"LE and JH were supported by the ERC Advanced Grant łRMTBeyondž No. 101020331","intvolume":"        28","article_type":"original","publication_identifier":{"eissn":["1095-0753"],"issn":["1095-0761"]},"volume":28,"doi":"10.4310/ATMP.241031013250","author":[{"orcid":"0000-0002-4901-7992","last_name":"Cipolloni","first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio"},{"first_name":"László","orcid":"0000-0001-5366-9603","last_name":"Erdös","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","full_name":"Henheik, Sven Joscha","last_name":"Henheik","orcid":"0000-0003-1106-327X","first_name":"Sven Joscha"}],"date_created":"2024-12-15T23:01:51Z","OA_place":"repository","scopus_import":"1","_id":"18656","citation":{"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.","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.","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>","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>.","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>.","short":"G. Cipolloni, L. Erdös, S.J. Henheik, Advances in Theoretical and Mathematical Physics 28 (2024) 2025–2083.","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>"},"arxiv":1,"oa":1,"date_published":"2024-10-30T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"ec_funded":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"type":"journal_article","year":"2024","publisher":"Elsevier","corr_author":"1","month":"08","issue":"4","day":"15","OA_type":"hybrid","related_material":{"record":[{"status":"public","id":"19540","relation":"dissertation_contains"}]},"language":[{"iso":"eng"}],"file":[{"file_id":"19891","checksum":"07d3f73e0c56e68eb110851842c22ee0","file_name":"2025_JourFunctionalAnalysis_Cipolloni.pdf","date_created":"2025-06-24T13:14:21Z","access_level":"open_access","creator":"dernst","relation":"main_file","content_type":"application/pdf","date_updated":"2025-06-24T13:14:21Z","file_size":1374854,"success":1}],"ddc":["510"],"date_updated":"2026-04-07T12:37:11Z","external_id":{"isi":["001325502400001"]},"article_number":"110495","status":"public","article_processing_charge":"Yes (via OA deal)","publication":"Journal of Functional Analysis","has_accepted_license":"1","isi":1,"department":[{"_id":"LaEr"}],"intvolume":"       287","acknowledgement":"Supported by ERC Advanced Grant “RMTBeyond” No. 101020331.\r\nSupported by the SNSF Ambizione Grant PZ00P2_209089.","volume":287,"publication_identifier":{"issn":["0022-1236"],"eissn":["1096-0783"]},"article_type":"original","date_created":"2024-05-26T22:00:57Z","doi":"10.1016/j.jfa.2024.110495","author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","last_name":"Cipolloni","first_name":"Giorgio"},{"first_name":"László","last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Henheik","orcid":"0000-0003-1106-327X","first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","full_name":"Henheik, Sven Joscha"},{"last_name":"Schröder","orcid":"0000-0002-2904-1856","first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","full_name":"Schröder, Dominik J"}],"_id":"17049","OA_place":"publisher","scopus_import":"1","oa":1,"date_published":"2024-08-15T00:00:00Z","citation":{"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.","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.","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>","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>","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>.","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>.","short":"G. Cipolloni, L. Erdös, S.J. Henheik, D.J. Schröder, Journal of Functional Analysis 287 (2024)."},"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","abstract":[{"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.","lang":"eng"}],"publication_status":"published","title":"Optimal lower bound on eigenvector overlaps for non-Hermitian random matrices","oa_version":"Published Version","file_date_updated":"2025-06-24T13:14:21Z","quality_controlled":"1"},{"abstract":[{"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.","lang":"eng"}],"publication_status":"draft","oa_version":"Preprint","title":"Eigenstate thermalisation at the edge for Wigner matrices","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2309.05488"}],"acknowledgement":"Supported by ERC Advanced Grant “RMTBeyond” No. 101020331.","doi":"10.48550/arXiv.2309.05488","author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio","last_name":"Cipolloni","orcid":"0000-0002-4901-7992","first_name":"Giorgio"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","last_name":"Erdös","orcid":"0000-0001-5366-9603","first_name":"László"},{"full_name":"Henheik, Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha","last_name":"Henheik","orcid":"0000-0003-1106-327X"}],"date_created":"2025-04-11T08:19:22Z","_id":"19545","OA_place":"repository","oa":1,"date_published":"2024-12-17T00:00:00Z","arxiv":1,"citation":{"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>","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>.","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>.","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>. .","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>."},"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","related_material":{"record":[{"relation":"dissertation_contains","id":"19540","status":"public"}]},"language":[{"iso":"eng"}],"date_updated":"2026-04-07T12:37:11Z","external_id":{"arxiv":["2309.05488"]},"status":"public","article_processing_charge":"No","publication":"arXiv","department":[{"_id":"LaEr"}],"ec_funded":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"type":"preprint","project":[{"grant_number":"101020331","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"year":"2024","corr_author":"1","month":"12","day":"17"},{"date_updated":"2026-04-07T12:37:11Z","publication_status":"draft","oa_version":"Preprint","title":"Response theory for locally gapped systems","language":[{"iso":"eng"}],"related_material":{"record":[{"relation":"dissertation_contains","id":"19540","status":"public"}]},"abstract":[{"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.","lang":"eng"}],"article_processing_charge":"No","department":[{"_id":"LaEr"}],"publication":"arXiv","external_id":{"arxiv":["2410.10809"]},"status":"public","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2410.10809","open_access":"1"}],"type":"preprint","year":"2024","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"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>.","ieee":"S. J. Henheik and T. Wessel, “Response theory for locally gapped systems,” <i>arXiv</i>. .","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>","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>.","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>"},"arxiv":1,"oa":1,"date_published":"2024-10-14T00:00:00Z","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","day":"14","doi":"10.48550/arXiv.2410.10809","author":[{"orcid":"0000-0003-1106-327X","last_name":"Henheik","first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","full_name":"Henheik, Sven Joscha"},{"last_name":"Wessel","first_name":"Tom","full_name":"Wessel, Tom"}],"date_created":"2025-04-11T11:54:56Z","OA_place":"repository","month":"10","_id":"19551","corr_author":"1"},{"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"year":"2024","type":"preprint","_id":"19550","corr_author":"1","OA_place":"repository","month":"10","author":[{"first_name":"Sven Joscha","orcid":"0000-0003-1106-327X","last_name":"Henheik","full_name":"Henheik, Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb"},{"full_name":"Langmann, Edwin","last_name":"Langmann","first_name":"Edwin"},{"full_name":"Lauritsen, Asbjørn Bækgaard","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1","first_name":"Asbjørn Bækgaard","orcid":"0000-0003-4476-2288","last_name":"Lauritsen"}],"date_created":"2025-04-11T11:43:58Z","doi":"10.48550/arXiv.2409.17297","day":"21","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","oa":1,"date_published":"2024-10-21T00:00:00Z","citation":{"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>","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>.","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>.","short":"S.J. Henheik, E. Langmann, A.B. Lauritsen, ArXiv (n.d.).","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>","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>.","ieee":"S. J. Henheik, E. Langmann, and A. B. Lauritsen, “Multi-band superconductors have enhanced critical temperatures,” <i>arXiv</i>. ."},"arxiv":1,"abstract":[{"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.","lang":"eng"}],"related_material":{"record":[{"id":"19540","status":"public","relation":"dissertation_contains"}]},"language":[{"iso":"eng"}],"oa_version":"Preprint","title":"Multi-band superconductors have enhanced critical temperatures","date_updated":"2026-04-07T12:37:11Z","publication_status":"draft","status":"public","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2409.17297","open_access":"1"}],"external_id":{"arxiv":["2409.17297"]},"publication":"arXiv","department":[{"_id":"LaEr"},{"_id":"RoSe"}],"article_processing_charge":"No"},{"day":"03","month":"11","corr_author":"1","year":"2024","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020"}],"type":"preprint","ec_funded":1,"department":[{"_id":"LaEr"}],"publication":"arXiv","article_processing_charge":"No","status":"public","external_id":{"arxiv":["2410.06813"]},"date_updated":"2026-04-07T12:37:11Z","language":[{"iso":"eng"}],"related_material":{"record":[{"relation":"later_version","id":"20322","status":"public"},{"id":"20575","status":"public","relation":"dissertation_contains"},{"id":"19540","status":"public","relation":"dissertation_contains"}]},"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","arxiv":1,"citation":{"ieee":"L. Erdös, S. J. Henheik, and V. Riabov, “Cusp universality for correlated random matrices,” <i>arXiv</i>. .","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>.","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>","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>","short":"L. Erdös, S.J. Henheik, V. Riabov, ArXiv (n.d.).","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>.","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>."},"oa":1,"date_published":"2024-11-03T00:00:00Z","OA_place":"repository","_id":"19547","author":[{"orcid":"0000-0001-5366-9603","last_name":"Erdös","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László"},{"full_name":"Henheik, Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha","orcid":"0000-0003-1106-327X","last_name":"Henheik"},{"last_name":"Riabov","first_name":"Volodymyr","id":"1949f904-edfb-11eb-afb5-e2dfddabb93b","full_name":"Riabov, Volodymyr"}],"date_created":"2025-04-11T08:48:21Z","doi":"10.48550/arXiv.2410.06813","acknowledgement":"Supported by the ERC Advanced Grant \"RMTBeyond\"\r\nNo. 101020331.","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2410.06813"}],"title":"Cusp universality for correlated random matrices","oa_version":"Preprint","publication_status":"draft","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"}]},{"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"}],"publication_status":"published","title":"Universality in low-dimensional BCS theory","oa_version":"Published Version","quality_controlled":"1","file_date_updated":"2025-01-09T07:56:28Z","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.","intvolume":"        36","article_type":"original","publication_identifier":{"issn":["0129-055X"],"eissn":["1793-6659"]},"volume":36,"doi":"10.1142/s0129055x2360005x","author":[{"id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","full_name":"Henheik, Sven Joscha","last_name":"Henheik","orcid":"0000-0003-1106-327X","first_name":"Sven Joscha"},{"orcid":"0000-0003-4476-2288","last_name":"Lauritsen","first_name":"Asbjørn Bækgaard","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1","full_name":"Lauritsen, Asbjørn Bækgaard"},{"full_name":"Roos, Barbara","id":"5DA90512-D80F-11E9-8994-2E2EE6697425","first_name":"Barbara","last_name":"Roos","orcid":"0000-0002-9071-5880"}],"date_created":"2023-11-15T23:48:14Z","OA_place":"publisher","scopus_import":"1","_id":"14542","arxiv":1,"citation":{"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>.","short":"S.J. Henheik, A.B. Lauritsen, B. Roos, Reviews in Mathematical Physics 36 (2024).","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>.","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>","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>","ista":"Henheik SJ, Lauritsen AB, Roos B. 2024. Universality in low-dimensional BCS theory. Reviews in Mathematical Physics. 36(9), 2360005.","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."},"oa":1,"date_published":"2024-10-01T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","language":[{"iso":"eng"}],"related_material":{"record":[{"relation":"dissertation_contains","id":"19540","status":"public"},{"id":"18135","status":"public","relation":"dissertation_contains"}]},"file":[{"content_type":"application/pdf","date_updated":"2025-01-09T07:56:28Z","file_size":503910,"success":1,"relation":"main_file","file_id":"18786","file_name":"2024_ReviewsmathPhysics_Henheik.pdf","date_created":"2025-01-09T07:56:28Z","checksum":"2b053a4223b4db14b90520999ec56054","access_level":"open_access","creator":"dernst"}],"ddc":["510"],"date_updated":"2026-04-07T13:01:40Z","article_number":"2360005 ","external_id":{"isi":["001099640300002"],"arxiv":["2301.05621"]},"status":"public","article_processing_charge":"Yes (in subscription journal)","has_accepted_license":"1","department":[{"_id":"GradSch"},{"_id":"LaEr"},{"_id":"RoSe"}],"isi":1,"publication":"Reviews in Mathematical Physics","ec_funded":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","grant_number":"101020331"},{"name":"Mathematical Challenges in BCS Theory of Superconductivity","grant_number":"I06427","_id":"bda63fe5-d553-11ed-ba76-a16e3d2f256b"}],"type":"journal_article","year":"2024","publisher":"World Scientific Publishing","month":"10","corr_author":"1","OA_type":"hybrid","issue":"9","day":"01"},{"publication_status":"published","title":"Central limit theorems for random matrices: From resolvents to free probability","oa_version":"Published Version","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."}],"file_date_updated":"2024-06-26T12:44:53Z","page":"206","alternative_title":["ISTA Thesis"],"publication_identifier":{"issn":["2663-337X"]},"citation":{"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>","short":"J. Reker, Central Limit Theorems for Random Matrices: From Resolvents to Free Probability, Institute of Science and Technology Austria, 2024.","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>.","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>.","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>","ista":"Reker J. 2024. Central limit theorems for random matrices: From resolvents to free probability. Institute of Science and Technology Austria.","ieee":"J. Reker, “Central limit theorems for random matrices: From resolvents to free probability,” Institute of Science and Technology Austria, 2024."},"supervisor":[{"full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","last_name":"Erdös","orcid":"0000-0001-5366-9603"}],"date_published":"2024-06-26T00:00:00Z","oa":1,"user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","date_created":"2024-06-24T11:23:29Z","doi":"10.15479/at:ista:17164","author":[{"last_name":"Reker","first_name":"Jana","id":"e796e4f9-dc8d-11ea-abe3-97e26a0323e9","full_name":"Reker, Jana"}],"OA_place":"publisher","_id":"17164","ddc":["519"],"date_updated":"2026-04-07T13:02:13Z","file":[{"creator":"jreker","access_level":"open_access","file_name":"ISTA_Thesis_JReker.pdf","checksum":"fb16d86e1f2753dc3a9e14d2bdfd84cd","date_created":"2024-06-26T12:39:36Z","file_id":"17176","relation":"main_file","date_updated":"2024-06-26T12:44:53Z","file_size":2783027,"content_type":"application/pdf"},{"file_id":"17177","file_name":"ISTA_Thesis_JReker_SourceFiles.zip","date_created":"2024-06-26T12:39:42Z","checksum":"cb1e54009d47c1dcf5b866c4566fa27f","creator":"jreker","access_level":"closed","relation":"source_file","date_updated":"2024-06-26T12:44:53Z","file_size":3054878,"content_type":"application/zip"}],"language":[{"iso":"eng"}],"related_material":{"record":[{"relation":"part_of_dissertation","status":"public","id":"17173"},{"status":"public","id":"11135","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","id":"17047","status":"public"},{"id":"17154","status":"public","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","status":"public","id":"17174"}]},"article_processing_charge":"No","has_accepted_license":"1","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"status":"public","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020"}],"type":"dissertation","year":"2024","ec_funded":1,"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode","image":"/images/cc_by_nc_sa.png","name":"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)","short":"CC BY-NC-SA (4.0)"},"keyword":["Random Matrices","Spectrum","Central Limit Theorem","Resolvent","Free Probability"],"degree_awarded":"PhD","license":"https://creativecommons.org/licenses/by-nc-sa/4.0/","day":"26","publisher":"Institute of Science and Technology Austria","month":"06","corr_author":"1"},{"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"}],"title":"Fluctuation moments for regular functions of Wigner Matrices","oa_version":"Published Version","publication_status":"published","quality_controlled":"1","file_date_updated":"2024-06-26T11:26:42Z","intvolume":"        27","article_type":"original","publication_identifier":{"eissn":["1572-9656"],"issn":["1385-0172"]},"volume":27,"scopus_import":"1","_id":"17154","author":[{"id":"e796e4f9-dc8d-11ea-abe3-97e26a0323e9","full_name":"Reker, Jana","last_name":"Reker","first_name":"Jana"}],"doi":"10.1007/s11040-024-09483-y","date_created":"2024-06-21T09:31:17Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","arxiv":1,"citation":{"ista":"Reker J. 2024. Fluctuation moments for regular functions of Wigner Matrices. Mathematical Physics, Analysis and Geometry. 27(3), 10.","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.","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>.","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>.","short":"J. Reker, Mathematical Physics, Analysis and Geometry 27 (2024).","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>","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>"},"oa":1,"date_published":"2024-06-20T00:00:00Z","language":[{"iso":"eng"}],"related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"17164"}]},"file":[{"relation":"main_file","access_level":"open_access","creator":"cchlebak","checksum":"7d04318d66f765621bdcb648378d458e","date_created":"2024-06-26T11:26:42Z","file_id":"17175","file_name":"2024_MathPhysAnaGeo_Reker.pdf","success":1,"content_type":"application/pdf","date_updated":"2024-06-26T11:26:42Z","file_size":1327596}],"date_updated":"2026-04-07T13:02:12Z","ddc":["519"],"status":"public","article_number":"10","external_id":{"isi":["001251464300001"],"arxiv":["2307.11029"]},"department":[{"_id":"LaEr"}],"has_accepted_license":"1","isi":1,"publication":"Mathematical Physics, Analysis and Geometry","article_processing_charge":"Yes (via OA deal)","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"ec_funded":1,"year":"2024","type":"journal_article","project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"},{"_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020"}],"month":"06","publisher":"Springer Nature","day":"20","issue":"3"},{"department":[{"_id":"GradSch"},{"_id":"LaEr"}],"isi":1,"publication":"Random Matrices: Theory and Applications","article_processing_charge":"No","status":"public","article_number":"2450007","external_id":{"isi":["001229295200002"],"arxiv":["2212.14638"]},"date_updated":"2026-04-07T13:02:12Z","language":[{"iso":"eng"}],"related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"17164"}]},"OA_type":"green","issue":"2","day":"01","month":"04","corr_author":"1","publisher":"World Scientific Publishing","year":"2024","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020"}],"type":"journal_article","ec_funded":1,"quality_controlled":"1","main_file_link":[{"url":" https://doi.org/10.48550/arXiv.2212.14638","open_access":"1"}],"oa_version":"Preprint","title":"Dynamics of a rank-one multiplicative perturbation of a unitary matrix","publication_status":"published","abstract":[{"lang":"eng","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."}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","arxiv":1,"citation":{"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>","short":"G. Dubach, J. Reker, Random Matrices: Theory and Applications 13 (2024).","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>.","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>.","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>","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.","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."},"date_published":"2024-04-01T00:00:00Z","oa":1,"OA_place":"repository","scopus_import":"1","_id":"17047","date_created":"2024-05-23T08:31:57Z","doi":"10.1142/s2010326324500072","author":[{"full_name":"Dubach, Guillaume","id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E","first_name":"Guillaume","last_name":"Dubach","orcid":"0000-0001-6892-8137"},{"id":"e796e4f9-dc8d-11ea-abe3-97e26a0323e9","full_name":"Reker, Jana","last_name":"Reker","first_name":"Jana"}],"article_type":"original","volume":13,"publication_identifier":{"issn":["2010-3263"],"eissn":["2010-3271"]},"intvolume":"        13"},{"article_processing_charge":"Yes (via OA deal)","isi":1,"has_accepted_license":"1","department":[{"_id":"LaEr"}],"publication":"Probability Theory and Related Fields","external_id":{"isi":["000830344500001"],"arxiv":["2106.10200"]},"status":"public","ddc":["510"],"date_updated":"2024-10-09T21:03:02Z","file":[{"success":1,"date_updated":"2023-08-14T12:47:32Z","file_size":782278,"content_type":"application/pdf","relation":"main_file","creator":"dernst","access_level":"open_access","file_name":"2023_ProbabilityTheory_Cipolloni.pdf","checksum":"b9247827dae5544d1d19c37abe547abc","file_id":"14054","date_created":"2023-08-14T12:47:32Z"}],"language":[{"iso":"eng"}],"day":"01","publisher":"Springer Nature","month":"04","corr_author":"1","type":"journal_article","year":"2023","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"file_date_updated":"2023-08-14T12:47:32Z","quality_controlled":"1","page":"1183–1218","publication_status":"published","oa_version":"Published Version","title":"Quenched universality for deformed Wigner matrices","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."}],"citation":{"short":"G. Cipolloni, L. Erdös, D.J. Schröder, Probability Theory and Related Fields 185 (2023) 1183–1218.","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>.","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>.","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>","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>","ista":"Cipolloni G, Erdös L, Schröder DJ. 2023. Quenched universality for deformed Wigner matrices. Probability Theory and Related Fields. 185, 1183–1218.","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."},"arxiv":1,"date_published":"2023-04-01T00:00:00Z","oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"full_name":"Cipolloni, Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio","last_name":"Cipolloni","orcid":"0000-0002-4901-7992"},{"full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","last_name":"Erdös","orcid":"0000-0001-5366-9603"},{"last_name":"Schröder","orcid":"0000-0002-2904-1856","first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","full_name":"Schröder, Dominik J"}],"doi":"10.1007/s00440-022-01156-7","date_created":"2022-08-07T22:02:00Z","scopus_import":"1","_id":"11741","article_type":"original","publication_identifier":{"issn":["0178-8051"],"eissn":["1432-2064"]},"volume":185,"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).","intvolume":"       185"},{"abstract":[{"text":"For large dimensional non-Hermitian random matrices X with real or complex independent, identically distributed, centered entries, we consider the fluctuations of f (X) as a matrix where f is an analytic function around the spectrum of X. We prove that for a generic bounded square matrix A, the quantity Tr f (X)A exhibits Gaussian fluctuations as the matrix size grows to infinity, which consists of two independent modes corresponding to the tracial and traceless parts of A. We find a new formula for the variance of the traceless part that involves the Frobenius norm of A and the L2-norm of f on the boundary of the limiting spectrum. ","lang":"eng"},{"text":"On étudie les fluctuations de f (X), où X est une matrice aléatoire non-hermitienne de grande taille à coefficients i.i.d. (réels ou complexes), et f une fonction analytique sur un domaine qui contient le spectre de X. On prouve que, pour une matrice carrée générique et bornée A, les fluctuations de la quantité tr f (X)A sont asymptotiquement gaussiennes et comportent deux modes indépendants, correspondant aux composantes traciale et de trace nulle de A. Une nouvelle formule est établie pour la variance de la composante de trace nulle, qui fait intervenir la norme de Frobenius de A et la norme L2 de f sur la frontière du spectre limite.","lang":"fre"}],"publication_status":"published","title":"Functional CLT for non-Hermitian random matrices","oa_version":"Preprint","page":"2083-2105","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2112.11382"}],"quality_controlled":"1","intvolume":"        59","acknowledgement":"The first author was partially supported by ERC Advanced Grant “RMTBeyond” No. 101020331. The second author was supported by ERC Advanced Grant “RMTBeyond” No. 101020331.\r\nThe authors are grateful to the anonymous referees and associated editor for carefully reading this paper and providing helpful comments that improved the quality of the article. Also the authors would like to thank Peter Forrester for pointing out the reference [12] that was absent in the previous version of the manuscript.","volume":59,"publication_identifier":{"issn":["0246-0203"]},"article_type":"original","author":[{"last_name":"Erdös","orcid":"0000-0001-5366-9603","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László"},{"last_name":"Ji","first_name":"Hong Chang","id":"dd216c0a-c1f9-11eb-beaf-e9ea9d2de76d","full_name":"Ji, Hong Chang"}],"date_created":"2023-12-10T23:01:00Z","doi":"10.1214/22-AIHP1304","_id":"14667","scopus_import":"1","oa":1,"date_published":"2023-11-01T00:00:00Z","citation":{"apa":"Erdös, L., &#38; Ji, H. C. (2023). Functional CLT for non-Hermitian random matrices. <i>Annales de l’institut Henri Poincare (B) Probability and Statistics</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/22-AIHP1304\">https://doi.org/10.1214/22-AIHP1304</a>","mla":"Erdös, László, and Hong Chang Ji. “Functional CLT for Non-Hermitian Random Matrices.” <i>Annales de l’institut Henri Poincare (B) Probability and Statistics</i>, vol. 59, no. 4, Institute of Mathematical Statistics, 2023, pp. 2083–105, doi:<a href=\"https://doi.org/10.1214/22-AIHP1304\">10.1214/22-AIHP1304</a>.","short":"L. Erdös, H.C. Ji, Annales de l’institut Henri Poincare (B) Probability and Statistics 59 (2023) 2083–2105.","chicago":"Erdös, László, and Hong Chang Ji. “Functional CLT for Non-Hermitian Random Matrices.” <i>Annales de l’institut Henri Poincare (B) Probability and Statistics</i>. Institute of Mathematical Statistics, 2023. <a href=\"https://doi.org/10.1214/22-AIHP1304\">https://doi.org/10.1214/22-AIHP1304</a>.","ama":"Erdös L, Ji HC. Functional CLT for non-Hermitian random matrices. <i>Annales de l’institut Henri Poincare (B) Probability and Statistics</i>. 2023;59(4):2083-2105. doi:<a href=\"https://doi.org/10.1214/22-AIHP1304\">10.1214/22-AIHP1304</a>","ieee":"L. Erdös and H. C. Ji, “Functional CLT for non-Hermitian random matrices,” <i>Annales de l’institut Henri Poincare (B) Probability and Statistics</i>, vol. 59, no. 4. Institute of Mathematical Statistics, pp. 2083–2105, 2023.","ista":"Erdös L, Ji HC. 2023. Functional CLT for non-Hermitian random matrices. Annales de l’institut Henri Poincare (B) Probability and Statistics. 59(4), 2083–2105."},"arxiv":1,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","language":[{"iso":"eng"}],"date_updated":"2025-09-09T13:41:08Z","external_id":{"isi":["001098456400010"],"arxiv":["2112.11382"]},"status":"public","article_processing_charge":"No","publication":"Annales de l'institut Henri Poincare (B) Probability and Statistics","department":[{"_id":"LaEr"}],"isi":1,"ec_funded":1,"type":"journal_article","project":[{"grant_number":"101020331","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"year":"2023","publisher":"Institute of Mathematical Statistics","corr_author":"1","month":"11","day":"01","issue":"4"},{"publication":"Electronic Communications in Probability","isi":1,"has_accepted_license":"1","department":[{"_id":"LaEr"}],"article_processing_charge":"No","status":"public","external_id":{"isi":["000950650200005"],"arxiv":["2108.13694"]},"ddc":["510"],"file":[{"date_created":"2023-02-27T09:43:27Z","file_name":"2023_ElectCommProbability_Dubach.pdf","checksum":"a1c6f0a3e33688fd71309c86a9aad86e","file_id":"12692","access_level":"open_access","creator":"dernst","relation":"main_file","date_updated":"2023-02-27T09:43:27Z","file_size":479105,"content_type":"application/pdf","success":1}],"date_updated":"2025-04-14T07:44:00Z","language":[{"iso":"eng"}],"day":"08","corr_author":"1","month":"02","publisher":"Institute of Mathematical Statistics","year":"2023","project":[{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425"},{"call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"type":"journal_article","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"ec_funded":1,"quality_controlled":"1","file_date_updated":"2023-02-27T09:43:27Z","page":"1-13","oa_version":"Published Version","title":"Dynamics of a rank-one perturbation of a Hermitian matrix","publication_status":"published","abstract":[{"text":"We study the eigenvalue trajectories of a time dependent matrix Gt=H+itvv∗ for t≥0, where H is an N×N Hermitian random matrix and v is a unit vector. In particular, we establish that with high probability, an outlier can be distinguished at all times t>1+N−1/3+ϵ, for any ϵ>0. The study of this natural process combines elements of Hermitian and non-Hermitian analysis, and illustrates some aspects of the intrinsic instability of (even weakly) non-Hermitian matrices.","lang":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"date_published":"2023-02-08T00:00:00Z","citation":{"ista":"Dubach G, Erdös L. 2023. Dynamics of a rank-one perturbation of a Hermitian matrix. Electronic Communications in Probability. 28, 1–13.","ieee":"G. Dubach and L. Erdös, “Dynamics of a rank-one perturbation of a Hermitian matrix,” <i>Electronic Communications in Probability</i>, vol. 28. Institute of Mathematical Statistics, pp. 1–13, 2023.","ama":"Dubach G, Erdös L. Dynamics of a rank-one perturbation of a Hermitian matrix. <i>Electronic Communications in Probability</i>. 2023;28:1-13. doi:<a href=\"https://doi.org/10.1214/23-ECP516\">10.1214/23-ECP516</a>","short":"G. Dubach, L. Erdös, Electronic Communications in Probability 28 (2023) 1–13.","chicago":"Dubach, Guillaume, and László Erdös. “Dynamics of a Rank-One Perturbation of a Hermitian Matrix.” <i>Electronic Communications in Probability</i>. Institute of Mathematical Statistics, 2023. <a href=\"https://doi.org/10.1214/23-ECP516\">https://doi.org/10.1214/23-ECP516</a>.","mla":"Dubach, Guillaume, and László Erdös. “Dynamics of a Rank-One Perturbation of a Hermitian Matrix.” <i>Electronic Communications in Probability</i>, vol. 28, Institute of Mathematical Statistics, 2023, pp. 1–13, doi:<a href=\"https://doi.org/10.1214/23-ECP516\">10.1214/23-ECP516</a>.","apa":"Dubach, G., &#38; Erdös, L. (2023). Dynamics of a rank-one perturbation of a Hermitian matrix. <i>Electronic Communications in Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/23-ECP516\">https://doi.org/10.1214/23-ECP516</a>"},"arxiv":1,"_id":"12683","scopus_import":"1","date_created":"2023-02-26T23:01:01Z","doi":"10.1214/23-ECP516","author":[{"id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E","full_name":"Dubach, Guillaume","orcid":"0000-0001-6892-8137","last_name":"Dubach","first_name":"Guillaume"},{"orcid":"0000-0001-5366-9603","last_name":"Erdös","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László"}],"volume":28,"publication_identifier":{"eissn":["1083-589X"]},"article_type":"original","intvolume":"        28","acknowledgement":"G. Dubach gratefully acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411. L. Erdős is supported by ERC Advanced Grant “RMTBeyond” No. 101020331."},{"article_type":"original","volume":29,"publication_identifier":{"issn":["1350-7265"]},"intvolume":"        29","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","arxiv":1,"citation":{"apa":"Erdös, L., &#38; Xu, Y. (2023). Small deviation estimates for the largest eigenvalue of Wigner matrices. <i>Bernoulli</i>. Bernoulli Society for Mathematical Statistics and Probability. <a href=\"https://doi.org/10.3150/22-BEJ1490\">https://doi.org/10.3150/22-BEJ1490</a>","ama":"Erdös L, Xu Y. Small deviation estimates for the largest eigenvalue of Wigner matrices. <i>Bernoulli</i>. 2023;29(2):1063-1079. doi:<a href=\"https://doi.org/10.3150/22-BEJ1490\">10.3150/22-BEJ1490</a>","short":"L. Erdös, Y. Xu, Bernoulli 29 (2023) 1063–1079.","mla":"Erdös, László, and Yuanyuan Xu. “Small Deviation Estimates for the Largest Eigenvalue of Wigner Matrices.” <i>Bernoulli</i>, vol. 29, no. 2, Bernoulli Society for Mathematical Statistics and Probability, 2023, pp. 1063–79, doi:<a href=\"https://doi.org/10.3150/22-BEJ1490\">10.3150/22-BEJ1490</a>.","chicago":"Erdös, László, and Yuanyuan Xu. “Small Deviation Estimates for the Largest Eigenvalue of Wigner Matrices.” <i>Bernoulli</i>. Bernoulli Society for Mathematical Statistics and Probability, 2023. <a href=\"https://doi.org/10.3150/22-BEJ1490\">https://doi.org/10.3150/22-BEJ1490</a>.","ieee":"L. Erdös and Y. Xu, “Small deviation estimates for the largest eigenvalue of Wigner matrices,” <i>Bernoulli</i>, vol. 29, no. 2. Bernoulli Society for Mathematical Statistics and Probability, pp. 1063–1079, 2023.","ista":"Erdös L, Xu Y. 2023. Small deviation estimates for the largest eigenvalue of Wigner matrices. Bernoulli. 29(2), 1063–1079."},"date_published":"2023-05-01T00:00:00Z","oa":1,"scopus_import":"1","_id":"12707","doi":"10.3150/22-BEJ1490","date_created":"2023-03-05T23:01:05Z","author":[{"last_name":"Erdös","orcid":"0000-0001-5366-9603","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László"},{"first_name":"Yuanyuan","orcid":"0000-0003-1559-1205","last_name":"Xu","full_name":"Xu, Yuanyuan","id":"7902bdb1-a2a4-11eb-a164-c9216f71aea3"}],"oa_version":"Preprint","title":"Small deviation estimates for the largest eigenvalue of Wigner matrices","publication_status":"published","abstract":[{"text":"We establish precise right-tail small deviation estimates for the largest eigenvalue of real symmetric and complex Hermitian matrices whose entries are independent random variables with uniformly bounded moments. The proof relies on a Green function comparison along a continuous interpolating matrix flow for a long time. Less precise estimates are also obtained in the left tail.","lang":"eng"}],"quality_controlled":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2112.12093"}],"page":"1063-1079","year":"2023","type":"journal_article","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","grant_number":"101020331"}],"ec_funded":1,"day":"01","issue":"2","month":"05","corr_author":"1","publisher":"Bernoulli Society for Mathematical Statistics and Probability","date_updated":"2025-04-14T07:57:19Z","language":[{"iso":"eng"}],"isi":1,"department":[{"_id":"LaEr"}],"publication":"Bernoulli","article_processing_charge":"No","status":"public","external_id":{"isi":["000947270100008"],"arxiv":["2112.12093 "]}},{"quality_controlled":"1","page":"447-489","main_file_link":[{"url":"https://arxiv.org/abs/2012.13218","open_access":"1"}],"publication_status":"published","title":"Functional central limit theorems for Wigner matrices","oa_version":"Preprint","abstract":[{"text":"We consider the fluctuations of regular functions f of a Wigner matrix W viewed as an entire matrix f (W). Going beyond the well-studied tracial mode, Trf (W), which is equivalent to the customary linear statistics of eigenvalues, we show that Trf (W)A is asymptotically normal for any nontrivial bounded deterministic matrix A. We identify three different and asymptotically independent modes of this fluctuation, corresponding to the tracial part, the traceless diagonal part and the off-diagonal part of f (W) in the entire mesoscopic regime, where we find that the off-diagonal modes fluctuate on a much smaller scale than the tracial mode. As a main motivation to study CLT in such generality on small mesoscopic scales, we determine\r\nthe fluctuations in the eigenstate thermalization hypothesis (Phys. Rev. A 43 (1991) 2046–2049), that is, prove that the eigenfunction overlaps with any deterministic matrix are asymptotically Gaussian after a small spectral averaging. Finally, in the macroscopic regime our result also generalizes (Zh. Mat. Fiz. Anal. Geom. 9 (2013) 536–581, 611, 615) to complex W and to all crossover ensembles in between. The main technical inputs are the recent\r\nmultiresolvent local laws with traceless deterministic matrices from the companion paper (Comm. Math. Phys. 388 (2021) 1005–1048).","lang":"eng"}],"citation":{"apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2023). Functional central limit theorems for Wigner matrices. <i>Annals of Applied Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/22-AAP1820\">https://doi.org/10.1214/22-AAP1820</a>","mla":"Cipolloni, Giorgio, et al. “Functional Central Limit Theorems for Wigner Matrices.” <i>Annals of Applied Probability</i>, vol. 33, no. 1, Institute of Mathematical Statistics, 2023, pp. 447–89, doi:<a href=\"https://doi.org/10.1214/22-AAP1820\">10.1214/22-AAP1820</a>.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Functional Central Limit Theorems for Wigner Matrices.” <i>Annals of Applied Probability</i>. Institute of Mathematical Statistics, 2023. <a href=\"https://doi.org/10.1214/22-AAP1820\">https://doi.org/10.1214/22-AAP1820</a>.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Annals of Applied Probability 33 (2023) 447–489.","ama":"Cipolloni G, Erdös L, Schröder DJ. Functional central limit theorems for Wigner matrices. <i>Annals of Applied Probability</i>. 2023;33(1):447-489. doi:<a href=\"https://doi.org/10.1214/22-AAP1820\">10.1214/22-AAP1820</a>","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Functional central limit theorems for Wigner matrices,” <i>Annals of Applied Probability</i>, vol. 33, no. 1. Institute of Mathematical Statistics, pp. 447–489, 2023.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2023. Functional central limit theorems for Wigner matrices. Annals of Applied Probability. 33(1), 447–489."},"arxiv":1,"date_published":"2023-02-01T00:00:00Z","oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2023-03-26T22:01:08Z","author":[{"first_name":"Giorgio","orcid":"0000-0002-4901-7992","last_name":"Cipolloni","full_name":"Cipolloni, Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0001-5366-9603","last_name":"Erdös","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László"},{"full_name":"Schröder, Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J","last_name":"Schröder","orcid":"0000-0002-2904-1856"}],"doi":"10.1214/22-AAP1820","scopus_import":"1","_id":"12761","article_type":"original","publication_identifier":{"issn":["1050-5164"]},"volume":33,"acknowledgement":"The second author is partially funded by the ERC Advanced Grant “RMTBEYOND” No. 101020331. The third author is supported by Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zürich Foundation.","intvolume":"        33","article_processing_charge":"No","isi":1,"department":[{"_id":"LaEr"}],"publication":"Annals of Applied Probability","external_id":{"isi":["000946432400015"],"arxiv":["2012.13218"]},"status":"public","date_updated":"2025-04-14T07:57:19Z","language":[{"iso":"eng"}],"day":"01","issue":"1","publisher":"Institute of Mathematical Statistics","month":"02","corr_author":"1","project":[{"call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"type":"journal_article","year":"2023","ec_funded":1},{"oa_version":"Published Version","title":"On the spectral form factor for random matrices","publication_status":"published","abstract":[{"lang":"eng","text":"In the physics literature the spectral form factor (SFF), the squared Fourier transform of the empirical eigenvalue density, is the most common tool to test universality for disordered quantum systems, yet previous mathematical results have been restricted only to two exactly solvable models (Forrester in J Stat Phys 183:33, 2021. https://doi.org/10.1007/s10955-021-02767-5, Commun Math Phys 387:215–235, 2021. https://doi.org/10.1007/s00220-021-04193-w). We rigorously prove the physics prediction on SFF up to an intermediate time scale for a large class of random matrices using a robust method, the multi-resolvent local laws. Beyond Wigner matrices we also consider the monoparametric ensemble and prove that universality of SFF can already be triggered by a single random parameter, supplementing the recently proven Wigner–Dyson universality (Cipolloni et al. in Probab Theory Relat Fields, 2021. https://doi.org/10.1007/s00440-022-01156-7) to larger spectral scales. Remarkably, extensive numerics indicates that our formulas correctly predict the SFF in the entire slope-dip-ramp regime, as customarily called in physics."}],"file_date_updated":"2023-10-04T12:09:18Z","quality_controlled":"1","page":"1665-1700","volume":401,"publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"article_type":"original","intvolume":"       401","acknowledgement":"We are grateful to the authors of [25] for sharing with us their insights and preliminary numerical results. We are especially thankful to Stephen Shenker for very valuable advice over several email communications. Helpful comments on the manuscript from Peter Forrester and from the anonymous referees are also acknowledged.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria).\r\nLászló Erdős: Partially supported by ERC Advanced Grant \"RMTBeyond\" No. 101020331. Dominik Schröder: Supported by Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zürich Foundation.","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_published":"2023-07-01T00:00:00Z","oa":1,"citation":{"apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2023). On the spectral form factor for random matrices. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-023-04692-y\">https://doi.org/10.1007/s00220-023-04692-y</a>","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “On the Spectral Form Factor for Random Matrices.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00220-023-04692-y\">https://doi.org/10.1007/s00220-023-04692-y</a>.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Communications in Mathematical Physics 401 (2023) 1665–1700.","mla":"Cipolloni, Giorgio, et al. “On the Spectral Form Factor for Random Matrices.” <i>Communications in Mathematical Physics</i>, vol. 401, Springer Nature, 2023, pp. 1665–700, doi:<a href=\"https://doi.org/10.1007/s00220-023-04692-y\">10.1007/s00220-023-04692-y</a>.","ama":"Cipolloni G, Erdös L, Schröder DJ. On the spectral form factor for random matrices. <i>Communications in Mathematical Physics</i>. 2023;401:1665-1700. doi:<a href=\"https://doi.org/10.1007/s00220-023-04692-y\">10.1007/s00220-023-04692-y</a>","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “On the spectral form factor for random matrices,” <i>Communications in Mathematical Physics</i>, vol. 401. Springer Nature, pp. 1665–1700, 2023.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2023. On the spectral form factor for random matrices. Communications in Mathematical Physics. 401, 1665–1700."},"_id":"12792","scopus_import":"1","date_created":"2023-04-02T22:01:11Z","doi":"10.1007/s00220-023-04692-y","author":[{"full_name":"Cipolloni, Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio","orcid":"0000-0002-4901-7992","last_name":"Cipolloni"},{"first_name":"László","last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Dominik J","last_name":"Schröder","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87"}],"date_updated":"2025-04-14T07:57:19Z","ddc":["510"],"file":[{"creator":"dernst","access_level":"open_access","file_id":"14397","checksum":"72057940f76654050ca84a221f21786c","file_name":"2023_CommMathPhysics_Cipolloni.pdf","date_created":"2023-10-04T12:09:18Z","relation":"main_file","success":1,"content_type":"application/pdf","file_size":859967,"date_updated":"2023-10-04T12:09:18Z"}],"language":[{"iso":"eng"}],"publication":"Communications in Mathematical Physics","isi":1,"has_accepted_license":"1","department":[{"_id":"LaEr"}],"article_processing_charge":"Yes (via OA deal)","status":"public","external_id":{"isi":["000957343500001"]},"year":"2023","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020"}],"type":"journal_article","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"ec_funded":1,"day":"01","corr_author":"1","month":"07","publisher":"Springer Nature"}]