[{"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2210.12060","open_access":"1"}],"oa":1,"quality_controlled":"1","scopus_import":"1","publisher":"Springer Nature","month":"09","abstract":[{"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 0Probability Theory and Related Fields. Springer Nature. https://doi.org/10.1007/s00440-023-01229-1","ama":"Cipolloni G, Erdös L, Schröder DJ. Mesoscopic central limit theorem for non-Hermitian random matrices. Probability Theory and Related Fields. 2023. doi:10.1007/s00440-023-01229-1","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Probability Theory and Related Fields (2023).","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Mesoscopic central limit theorem for non-Hermitian random matrices,” Probability Theory and Related Fields. Springer Nature, 2023.","mla":"Cipolloni, Giorgio, et al. “Mesoscopic Central Limit Theorem for Non-Hermitian Random Matrices.” Probability Theory and Related Fields, Springer Nature, 2023, doi:10.1007/s00440-023-01229-1.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2023. Mesoscopic central limit theorem for non-Hermitian random matrices. Probability Theory and Related Fields.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Mesoscopic Central Limit Theorem for Non-Hermitian Random Matrices.” Probability Theory and Related Fields. Springer Nature, 2023. https://doi.org/10.1007/s00440-023-01229-1."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"scopus_import":"1","month":"02","intvolume":" 28","abstract":[{"lang":"eng","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."}],"oa_version":"Published Version","volume":28,"ec_funded":1,"license":"https://creativecommons.org/licenses/by/4.0/","publication_identifier":{"eissn":["1083-589X"]},"publication_status":"published","file":[{"date_updated":"2023-02-27T09:43:27Z","file_size":479105,"creator":"dernst","date_created":"2023-02-27T09:43:27Z","file_name":"2023_ElectCommProbability_Dubach.pdf","content_type":"application/pdf","access_level":"open_access","relation":"main_file","file_id":"12692","checksum":"a1c6f0a3e33688fd71309c86a9aad86e","success":1}],"language":[{"iso":"eng"}],"article_type":"original","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","_id":"12683","department":[{"_id":"LaEr"}],"file_date_updated":"2023-02-27T09:43:27Z","date_updated":"2023-10-17T12:48:10Z","ddc":["510"],"publisher":"Institute of Mathematical Statistics","quality_controlled":"1","oa":1,"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.","page":"1-13","doi":"10.1214/23-ECP516","date_published":"2023-02-08T00:00:00Z","date_created":"2023-02-26T23:01:01Z","isi":1,"has_accepted_license":"1","year":"2023","day":"08","publication":"Electronic Communications in Probability","project":[{"name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425"},{"name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"}],"author":[{"id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E","first_name":"Guillaume","full_name":"Dubach, Guillaume","orcid":"0000-0001-6892-8137","last_name":"Dubach"},{"last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László"}],"external_id":{"arxiv":["2108.13694"],"isi":["000950650200005"]},"article_processing_charge":"No","title":"Dynamics of a rank-one perturbation of a Hermitian matrix","citation":{"mla":"Dubach, Guillaume, and László Erdös. “Dynamics of a Rank-One Perturbation of a Hermitian Matrix.” Electronic Communications in Probability, vol. 28, Institute of Mathematical Statistics, 2023, pp. 1–13, doi:10.1214/23-ECP516.","ama":"Dubach G, Erdös L. Dynamics of a rank-one perturbation of a Hermitian matrix. Electronic Communications in Probability. 2023;28:1-13. doi:10.1214/23-ECP516","apa":"Dubach, G., & Erdös, L. (2023). Dynamics of a rank-one perturbation of a Hermitian matrix. Electronic Communications in Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/23-ECP516","ieee":"G. Dubach and L. Erdös, “Dynamics of a rank-one perturbation of a Hermitian matrix,” Electronic Communications in Probability, vol. 28. Institute of Mathematical Statistics, pp. 1–13, 2023.","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.” Electronic Communications in Probability. Institute of Mathematical Statistics, 2023. https://doi.org/10.1214/23-ECP516.","ista":"Dubach G, Erdös L. 2023. Dynamics of a rank-one perturbation of a Hermitian matrix. Electronic Communications in Probability. 28, 1–13."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"date_updated":"2023-10-17T12:48:52Z","department":[{"_id":"LaEr"}],"_id":"12761","type":"journal_article","article_type":"original","status":"public","publication_identifier":{"issn":["1050-5164"]},"publication_status":"published","language":[{"iso":"eng"}],"issue":"1","volume":33,"ec_funded":1,"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"}],"oa_version":"Preprint","scopus_import":"1","main_file_link":[{"url":"https://arxiv.org/abs/2012.13218","open_access":"1"}],"month":"02","intvolume":" 33","citation":{"mla":"Cipolloni, Giorgio, et al. “Functional Central Limit Theorems for Wigner Matrices.” Annals of Applied Probability, vol. 33, no. 1, Institute of Mathematical Statistics, 2023, pp. 447–89, doi:10.1214/22-AAP1820.","apa":"Cipolloni, G., Erdös, L., & Schröder, D. J. (2023). Functional central limit theorems for Wigner matrices. Annals of Applied Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/22-AAP1820","ama":"Cipolloni G, Erdös L, Schröder DJ. Functional central limit theorems for Wigner matrices. Annals of Applied Probability. 2023;33(1):447-489. doi:10.1214/22-AAP1820","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Annals of Applied Probability 33 (2023) 447–489.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Functional central limit theorems for Wigner matrices,” Annals of Applied Probability, vol. 33, no. 1. Institute of Mathematical Statistics, pp. 447–489, 2023.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Functional Central Limit Theorems for Wigner Matrices.” Annals of Applied Probability. Institute of Mathematical Statistics, 2023. https://doi.org/10.1214/22-AAP1820.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2023. Functional central limit theorems for Wigner matrices. Annals of Applied Probability. 33(1), 447–489."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio","full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","last_name":"Cipolloni"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","last_name":"Erdös","full_name":"Erdös, László","orcid":"0000-0001-5366-9603"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J","full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","last_name":"Schröder"}],"external_id":{"isi":["000946432400015"],"arxiv":["2012.13218"]},"article_processing_charge":"No","title":"Functional central limit theorems for Wigner matrices","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"}],"isi":1,"year":"2023","day":"01","publication":"Annals of Applied Probability","page":"447-489","doi":"10.1214/22-AAP1820","date_published":"2023-02-01T00:00:00Z","date_created":"2023-03-26T22:01:08Z","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.","publisher":"Institute of Mathematical Statistics","quality_controlled":"1","oa":1},{"title":"Universality in low-dimensional BCS theory","external_id":{"arxiv":["2301.05621"]},"article_processing_charge":"Yes (in subscription journal)","author":[{"last_name":"Henheik","orcid":"0000-0003-1106-327X","full_name":"Henheik, Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha"},{"orcid":"0000-0003-4476-2288","full_name":"Lauritsen, Asbjørn Bækgaard","last_name":"Lauritsen","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1","first_name":"Asbjørn Bækgaard"},{"id":"5DA90512-D80F-11E9-8994-2E2EE6697425","first_name":"Barbara","last_name":"Roos","orcid":"0000-0002-9071-5880","full_name":"Roos, Barbara"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"mla":"Henheik, Sven Joscha, et al. “Universality in Low-Dimensional BCS Theory.” Reviews in Mathematical Physics, 2360005, World Scientific Publishing, 2023, doi:10.1142/s0129055x2360005x.","ieee":"S. J. Henheik, A. B. Lauritsen, and B. Roos, “Universality in low-dimensional BCS theory,” Reviews in Mathematical Physics. World Scientific Publishing, 2023.","short":"S.J. Henheik, A.B. Lauritsen, B. Roos, Reviews in Mathematical Physics (2023).","ama":"Henheik SJ, Lauritsen AB, Roos B. Universality in low-dimensional BCS theory. Reviews in Mathematical Physics. 2023. doi:10.1142/s0129055x2360005x","apa":"Henheik, S. J., Lauritsen, A. B., & Roos, B. (2023). Universality in low-dimensional BCS theory. Reviews in Mathematical Physics. World Scientific Publishing. https://doi.org/10.1142/s0129055x2360005x","chicago":"Henheik, Sven Joscha, Asbjørn Bækgaard Lauritsen, and Barbara Roos. “Universality in Low-Dimensional BCS Theory.” Reviews in Mathematical Physics. World Scientific Publishing, 2023. https://doi.org/10.1142/s0129055x2360005x.","ista":"Henheik SJ, Lauritsen AB, Roos B. 2023. Universality in low-dimensional BCS theory. Reviews in Mathematical Physics., 2360005."},"project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d"},{"grant_number":"I06427","name":"Mathematical Challenges in BCS Theory of Superconductivity","_id":"bda63fe5-d553-11ed-ba76-a16e3d2f256b"}],"article_number":"2360005 ","date_created":"2023-11-15T23:48:14Z","doi":"10.1142/s0129055x2360005x","date_published":"2023-10-31T00:00:00Z","publication":"Reviews in Mathematical Physics","day":"31","year":"2023","has_accepted_license":"1","oa":1,"quality_controlled":"1","publisher":"World Scientific Publishing","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.","department":[{"_id":"GradSch"},{"_id":"LaEr"},{"_id":"RoSe"}],"date_updated":"2023-11-20T10:04:38Z","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","type":"journal_article","_id":"14542","ec_funded":1,"language":[{"iso":"eng"}],"publication_status":"epub_ahead","publication_identifier":{"issn":["0129-055X"],"eissn":["1793-6659"]},"month":"10","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1142/S0129055X2360005X"}],"scopus_import":"1","oa_version":"Published Version","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":"Annales de l'institut Henri Poincare (B) Probability and Statistics","day":"01","year":"2023","date_created":"2023-12-10T23:01:00Z","date_published":"2023-11-01T00:00:00Z","doi":"10.1214/22-AIHP1304","page":"2083-2105","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.","oa":1,"publisher":"Institute of Mathematical Statistics","quality_controlled":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ieee":"L. Erdös and H. C. Ji, “Functional CLT for non-Hermitian random matrices,” Annales de l’institut Henri Poincare (B) Probability and Statistics, vol. 59, no. 4. Institute of Mathematical Statistics, pp. 2083–2105, 2023.","short":"L. Erdös, H.C. Ji, Annales de l’institut Henri Poincare (B) Probability and Statistics 59 (2023) 2083–2105.","apa":"Erdös, L., & Ji, H. C. (2023). Functional CLT for non-Hermitian random matrices. Annales de l’institut Henri Poincare (B) Probability and Statistics. Institute of Mathematical Statistics. https://doi.org/10.1214/22-AIHP1304","ama":"Erdös L, Ji HC. Functional CLT for non-Hermitian random matrices. Annales de l’institut Henri Poincare (B) Probability and Statistics. 2023;59(4):2083-2105. doi:10.1214/22-AIHP1304","mla":"Erdös, László, and Hong Chang Ji. “Functional CLT for Non-Hermitian Random Matrices.” Annales de l’institut Henri Poincare (B) Probability and Statistics, vol. 59, no. 4, Institute of Mathematical Statistics, 2023, pp. 2083–105, doi:10.1214/22-AIHP1304.","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.","chicago":"Erdös, László, and Hong Chang Ji. “Functional CLT for Non-Hermitian Random Matrices.” Annales de l’institut Henri Poincare (B) Probability and Statistics. Institute of Mathematical Statistics, 2023. https://doi.org/10.1214/22-AIHP1304."},"title":"Functional CLT for non-Hermitian random matrices","external_id":{"arxiv":["2112.11382"]},"article_processing_charge":"No","author":[{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Ji, Hong Chang","last_name":"Ji","id":"dd216c0a-c1f9-11eb-beaf-e9ea9d2de76d","first_name":"Hong Chang"}],"project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["0246-0203"]},"ec_funded":1,"issue":"4","volume":59,"oa_version":"Preprint","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"},{"lang":"fre","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."}],"intvolume":" 59","month":"11","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2112.11382"}],"scopus_import":"1","date_updated":"2023-12-11T12:36:56Z","department":[{"_id":"LaEr"}],"_id":"14667","status":"public","article_type":"original","type":"journal_article"}]