[{"publication":"Bernoulli","type":"journal_article","issue":"2","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","call_identifier":"H2020"}],"publication_identifier":{"issn":["1350-7265"]},"article_processing_charge":"No","title":"Small deviation estimates for the largest eigenvalue of Wigner matrices","date_published":"2023-05-01T00:00:00Z","fulldoi":"https://doi.org/10.3150/22-BEJ1490","isi":1,"publisher":"Bernoulli Society for Mathematical Statistics and Probability","year":"2023","doi":"10.3150/22-BEJ1490","department":[{"_id":"LaEr"}],"date_created":"2023-03-05T23:01:05Z","author":[{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","full_name":"Erdös, László","first_name":"László","orcid":"0000-0001-5366-9603"},{"full_name":"Xu, Yuanyuan","last_name":"Xu","id":"7902bdb1-a2a4-11eb-a164-c9216f71aea3","orcid":"0000-0003-1559-1205","first_name":"Yuanyuan"}],"corr_author":"1","date_updated":"2025-04-14T07:57:19Z","month":"05","oa_version":"Preprint","volume":29,"page":"1063-1079","_id":"12707","publication_status":"published","quality_controlled":"1","scopus_import":"1","external_id":{"arxiv":["2112.12093 "],"isi":["000947270100008"]},"language":[{"iso":"eng"}],"oa":1,"intvolume":"        29","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"}],"ec_funded":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2112.12093"}],"arxiv":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","citation":{"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>.","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>","ista":"Erdös L, Xu Y. 2023. Small deviation estimates for the largest eigenvalue of Wigner matrices. Bernoulli. 29(2), 1063–1079.","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.","short":"L. Erdös, Y. Xu, Bernoulli 29 (2023) 1063–1079.","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>","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>."},"article_type":"original","day":"01"},{"publication_identifier":{"issn":["1050-5164"]},"article_processing_charge":"No","title":"Functional central limit theorems for Wigner matrices","publisher":"Institute of Mathematical Statistics","date_published":"2023-02-01T00:00:00Z","isi":1,"fulldoi":"https://doi.org/10.1214/22-AAP1820","type":"journal_article","issue":"1","publication":"Annals of Applied Probability","project":[{"call_identifier":"H2020","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"month":"02","oa_version":"Preprint","date_updated":"2025-04-14T07:57:19Z","corr_author":"1","_id":"12761","volume":33,"page":"447-489","doi":"10.1214/22-AAP1820","department":[{"_id":"LaEr"}],"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.","year":"2023","author":[{"first_name":"Giorgio","orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","last_name":"Cipolloni","full_name":"Cipolloni, Giorgio"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","full_name":"Erdös, László","first_name":"László","orcid":"0000-0001-5366-9603"},{"last_name":"Schröder","id":"408ED176-F248-11E8-B48F-1D18A9856A87","full_name":"Schröder, Dominik J","first_name":"Dominik J","orcid":"0000-0002-2904-1856"}],"date_created":"2023-03-26T22:01:08Z","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"}],"intvolume":"        33","publication_status":"published","language":[{"iso":"eng"}],"external_id":{"isi":["000946432400015"],"arxiv":["2012.13218"]},"oa":1,"scopus_import":"1","quality_controlled":"1","day":"01","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>","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.","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.","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>","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>."},"status":"public","article_type":"original","ec_funded":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2012.13218"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","arxiv":1},{"language":[{"iso":"eng"}],"external_id":{"isi":["000957343500001"]},"oa":1,"scopus_import":"1","quality_controlled":"1","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."}],"intvolume":"       401","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file":[{"success":1,"relation":"main_file","checksum":"72057940f76654050ca84a221f21786c","date_created":"2023-10-04T12:09:18Z","file_name":"2023_CommMathPhysics_Cipolloni.pdf","date_updated":"2023-10-04T12:09:18Z","file_size":859967,"access_level":"open_access","creator":"dernst","content_type":"application/pdf","file_id":"14397"}],"ec_funded":1,"has_accepted_license":"1","file_date_updated":"2023-10-04T12:09:18Z","day":"01","status":"public","citation":{"short":"G. Cipolloni, L. Erdös, D.J. Schröder, Communications in Mathematical Physics 401 (2023) 1665–1700.","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.","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>.","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>.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2023. On the spectral form factor for random matrices. Communications in Mathematical Physics. 401, 1665–1700.","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>"},"article_type":"original","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","call_identifier":"H2020"}],"type":"journal_article","publication":"Communications in Mathematical Physics","ddc":["510"],"publisher":"Springer Nature","date_published":"2023-07-01T00:00:00Z","fulldoi":"https://doi.org/10.1007/s00220-023-04692-y","isi":1,"publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"article_processing_charge":"Yes (via OA deal)","title":"On the spectral form factor for random matrices","author":[{"full_name":"Cipolloni, Giorgio","last_name":"Cipolloni","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992","first_name":"Giorgio"},{"orcid":"0000-0001-5366-9603","first_name":"László","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös"},{"full_name":"Schröder, Dominik J","last_name":"Schröder","id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856","first_name":"Dominik J"}],"date_created":"2023-04-02T22:01:11Z","doi":"10.1007/s00220-023-04692-y","department":[{"_id":"LaEr"}],"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.","year":"2023","_id":"12792","page":"1665-1700","volume":401,"month":"07","tmp":{"short":"CC BY (4.0)","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)"},"date_updated":"2025-04-14T07:57:19Z","oa_version":"Published Version","corr_author":"1"},{"publication":"Annales de l'institut Henri Poincare (B) Probability and Statistics","issue":"4","type":"journal_article","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","grant_number":"101020331"}],"title":"Functional CLT for non-Hermitian random matrices","article_processing_charge":"No","publication_identifier":{"issn":["0246-0203"]},"fulldoi":"https://doi.org/10.1214/22-AIHP1304","isi":1,"date_published":"2023-11-01T00:00:00Z","publisher":"Institute of Mathematical Statistics","year":"2023","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.","department":[{"_id":"LaEr"}],"doi":"10.1214/22-AIHP1304","date_created":"2023-12-10T23:01:00Z","author":[{"orcid":"0000-0001-5366-9603","first_name":"László","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös"},{"id":"dd216c0a-c1f9-11eb-beaf-e9ea9d2de76d","last_name":"Ji","full_name":"Ji, Hong Chang","first_name":"Hong Chang"}],"corr_author":"1","date_updated":"2025-09-09T13:41:08Z","oa_version":"Preprint","month":"11","volume":59,"page":"2083-2105","_id":"14667","publication_status":"published","quality_controlled":"1","scopus_import":"1","oa":1,"language":[{"iso":"eng"}],"external_id":{"isi":["001098456400010"],"arxiv":["2112.11382"]},"intvolume":"        59","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"}],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2112.11382"}],"ec_funded":1,"arxiv":1,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","article_type":"original","citation":{"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.","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>","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>.","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>.","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>","short":"L. Erdös, H.C. Ji, Annales de l’institut Henri Poincare (B) Probability and Statistics 59 (2023) 2083–2105.","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."},"status":"public","day":"01"},{"department":[{"_id":"LaEr"}],"doi":"10.1214/22-aap1882","year":"2023","acknowledgement":"The first author is partially supported by NSF Grant DMS-2113489 and grateful for the AMS-SIMONS travel grant (2020–2023). The second author is supported by the ERC Advanced Grant “RMTBeyond” No. 101020331.\r\nThe authors would like to thank the Editor, Associate Editor and an anonymous referee for their many critical suggestions which have significantly improved the paper. We also want to thank Zhigang Bao and Ji Oon Lee for many helpful discussions and comments.","author":[{"first_name":"Xiucai","full_name":"Ding, Xiucai","last_name":"Ding"},{"full_name":"Ji, Hong Chang","id":"dd216c0a-c1f9-11eb-beaf-e9ea9d2de76d","last_name":"Ji","first_name":"Hong Chang"}],"date_created":"2024-01-08T13:03:18Z","oa_version":"Preprint","date_updated":"2025-09-09T14:12:00Z","month":"08","corr_author":"1","_id":"14750","volume":33,"page":"2981-3009","issue":"4","type":"journal_article","publication":"The Annals of Applied Probability","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","grant_number":"101020331"}],"title":"Local laws for multiplication of random matrices","article_processing_charge":"No","publication_identifier":{"issn":["1050-5164"]},"publisher":"Institute of Mathematical Statistics","fulldoi":"https://doi.org/10.1214/22-aap1882","isi":1,"date_published":"2023-08-01T00:00:00Z","ec_funded":1,"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2010.16083"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","arxiv":1,"day":"01","article_type":"original","status":"public","citation":{"ista":"Ding X, Ji HC. 2023. Local laws for multiplication of random matrices. The Annals of Applied Probability. 33(4), 2981–3009.","ama":"Ding X, Ji HC. Local laws for multiplication of random matrices. <i>The Annals of Applied Probability</i>. 2023;33(4):2981-3009. doi:<a href=\"https://doi.org/10.1214/22-aap1882\">10.1214/22-aap1882</a>","mla":"Ding, Xiucai, and Hong Chang Ji. “Local Laws for Multiplication of Random Matrices.” <i>The Annals of Applied Probability</i>, vol. 33, no. 4, Institute of Mathematical Statistics, 2023, pp. 2981–3009, doi:<a href=\"https://doi.org/10.1214/22-aap1882\">10.1214/22-aap1882</a>.","chicago":"Ding, Xiucai, and Hong Chang Ji. “Local Laws for Multiplication of Random Matrices.” <i>The Annals of Applied Probability</i>. Institute of Mathematical Statistics, 2023. <a href=\"https://doi.org/10.1214/22-aap1882\">https://doi.org/10.1214/22-aap1882</a>.","apa":"Ding, X., &#38; Ji, H. C. (2023). Local laws for multiplication of random matrices. <i>The Annals of Applied Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/22-aap1882\">https://doi.org/10.1214/22-aap1882</a>","short":"X. Ding, H.C. Ji, The Annals of Applied Probability 33 (2023) 2981–3009.","ieee":"X. Ding and H. C. Ji, “Local laws for multiplication of random matrices,” <i>The Annals of Applied Probability</i>, vol. 33, no. 4. Institute of Mathematical Statistics, pp. 2981–3009, 2023."},"publication_status":"published","oa":1,"keyword":["Statistics","Probability and Uncertainty","Statistics and Probability"],"external_id":{"arxiv":["2010.16083"],"isi":["001031710500012"]},"language":[{"iso":"eng"}],"quality_controlled":"1","scopus_import":"1","abstract":[{"lang":"eng","text":"Consider the random matrix model A1/2UBU∗A1/2, where A and B are two N × N deterministic matrices and U is either an N × N Haar unitary or orthogonal random matrix. It is well known that on the macroscopic scale (Invent. Math. 104 (1991) 201–220), the limiting empirical spectral distribution (ESD) of the above model is given by the free multiplicative convolution\r\nof the limiting ESDs of A and B, denoted as μα \u0002 μβ, where μα and μβ are the limiting ESDs of A and B, respectively. In this paper, we study the asymptotic microscopic behavior of the edge eigenvalues and eigenvectors statistics. We prove that both the density of μA \u0002μB, where μA and μB are the ESDs of A and B, respectively and the associated subordination functions\r\nhave a regular behavior near the edges. Moreover, we establish the local laws near the edges on the optimal scale. In particular, we prove that the entries of the resolvent are close to some functionals depending only on the eigenvalues of A, B and the subordination functions with optimal convergence rates. Our proofs and calculations are based on the techniques developed for the additive model A+UBU∗ in (J. Funct. Anal. 271 (2016) 672–719; Comm. Math.\r\nPhys. 349 (2017) 947–990; Adv. Math. 319 (2017) 251–291; J. Funct. Anal. 279 (2020) 108639), and our results can be regarded as the counterparts of (J. Funct. Anal. 279 (2020) 108639) for the multiplicative model. "}],"intvolume":"        33"},{"article_type":"original","status":"public","citation":{"ista":"Schnelli K, Xu Y. 2023. Convergence rate to the Tracy–Widom laws for the largest eigenvalue of sample covariance matrices. The Annals of Applied Probability. 33(1), 677–725.","ama":"Schnelli K, Xu Y. Convergence rate to the Tracy–Widom laws for the largest eigenvalue of sample covariance matrices. <i>The Annals of Applied Probability</i>. 2023;33(1):677-725. doi:<a href=\"https://doi.org/10.1214/22-aap1826\">10.1214/22-aap1826</a>","mla":"Schnelli, Kevin, and Yuanyuan Xu. “Convergence Rate to the Tracy–Widom Laws for the Largest Eigenvalue of Sample Covariance Matrices.” <i>The Annals of Applied Probability</i>, vol. 33, no. 1, Institute of Mathematical Statistics, 2023, pp. 677–725, doi:<a href=\"https://doi.org/10.1214/22-aap1826\">10.1214/22-aap1826</a>.","apa":"Schnelli, K., &#38; Xu, Y. (2023). Convergence rate to the Tracy–Widom laws for the largest eigenvalue of sample covariance matrices. <i>The Annals of Applied Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/22-aap1826\">https://doi.org/10.1214/22-aap1826</a>","chicago":"Schnelli, Kevin, and Yuanyuan Xu. “Convergence Rate to the Tracy–Widom Laws for the Largest Eigenvalue of Sample Covariance Matrices.” <i>The Annals of Applied Probability</i>. Institute of Mathematical Statistics, 2023. <a href=\"https://doi.org/10.1214/22-aap1826\">https://doi.org/10.1214/22-aap1826</a>.","short":"K. Schnelli, Y. Xu, The Annals of Applied Probability 33 (2023) 677–725.","ieee":"K. Schnelli and Y. Xu, “Convergence rate to the Tracy–Widom laws for the largest eigenvalue of sample covariance matrices,” <i>The Annals of Applied Probability</i>, vol. 33, no. 1. Institute of Mathematical Statistics, pp. 677–725, 2023."},"day":"01","arxiv":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","ec_funded":1,"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2108.02728"}],"intvolume":"        33","abstract":[{"lang":"eng","text":"We establish a quantitative version of the Tracy–Widom law for the largest eigenvalue of high-dimensional sample covariance matrices. To be precise, we show that the fluctuations of the largest eigenvalue of a sample covariance matrix X∗X converge to its Tracy–Widom limit at a rate nearly N−1/3, where X is an M×N random matrix whose entries are independent real or complex random variables, assuming that both M and N tend to infinity at a constant rate. This result improves the previous estimate N−2/9 obtained by Wang (2019). Our proof relies on a Green function comparison method (Adv. Math. 229 (2012) 1435–1515) using iterative cumulant expansions, the local laws for the Green function and asymptotic properties of the correlation kernel of the white Wishart ensemble."}],"quality_controlled":"1","scopus_import":"1","oa":1,"language":[{"iso":"eng"}],"external_id":{"isi":["000946432400021"],"arxiv":["2108.02728"]},"keyword":["Statistics","Probability and Uncertainty","Statistics and Probability"],"publication_status":"published","page":"677-725","volume":33,"_id":"14775","corr_author":"1","oa_version":"Preprint","date_updated":"2025-04-14T07:57:19Z","month":"02","date_created":"2024-01-10T09:23:31Z","author":[{"orcid":"0000-0003-0954-3231","first_name":"Kevin","full_name":"Schnelli, Kevin","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","last_name":"Schnelli"},{"full_name":"Xu, Yuanyuan","id":"7902bdb1-a2a4-11eb-a164-c9216f71aea3","last_name":"Xu","orcid":"0000-0003-1559-1205","first_name":"Yuanyuan"}],"year":"2023","acknowledgement":"K. Schnelli was supported by the Swedish Research Council Grants VR-2017-05195, and the Knut and Alice Wallenberg Foundation. Y. Xu was supported by the Swedish Research Council Grant VR-2017-05195 and the ERC Advanced Grant “RMTBeyond” No. 101020331.","department":[{"_id":"LaEr"}],"doi":"10.1214/22-aap1826","fulldoi":"https://doi.org/10.1214/22-aap1826","isi":1,"date_published":"2023-02-01T00:00:00Z","publisher":"Institute of Mathematical Statistics","article_processing_charge":"No","title":"Convergence rate to the Tracy–Widom laws for the largest eigenvalue of sample covariance matrices","publication_identifier":{"issn":["1050-5164"]},"project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"publication":"The Annals of Applied Probability","issue":"1","type":"journal_article"},{"month":"09","tmp":{"short":"CC BY (4.0)","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)"},"oa_version":"Published Version","date_updated":"2025-07-16T08:01:03Z","volume":163,"page":"25-60","_id":"14780","year":"2023","acknowledgement":"The authors would like to thank the editor, the associated editor and two anonymous referees for their many critical suggestions which have significantly improved the paper. The authors are also grateful to Zhigang Bao and Ji Oon Lee for many helpful discussions. The first author also wants to thank Hari Bercovici for many useful comments. The first author is partially supported by National Science Foundation DMS-2113489 and the second author is supported by ERC Advanced Grant “RMTBeyond” No. 101020331.","department":[{"_id":"LaEr"}],"doi":"10.1016/j.spa.2023.05.009","date_created":"2024-01-10T09:29:25Z","author":[{"first_name":"Xiucai","last_name":"Ding","full_name":"Ding, Xiucai"},{"full_name":"Ji, Hong Chang","id":"dd216c0a-c1f9-11eb-beaf-e9ea9d2de76d","last_name":"Ji","first_name":"Hong Chang"}],"title":"Spiked multiplicative random matrices and principal components","article_processing_charge":"Yes (in subscription journal)","publication_identifier":{"issn":["0304-4149"],"eissn":["1879-209X"]},"fulldoi":"https://doi.org/10.1016/j.spa.2023.05.009","isi":1,"date_published":"2023-09-01T00:00:00Z","ddc":["510"],"publisher":"Elsevier","publication":"Stochastic Processes and their Applications","type":"journal_article","project":[{"grant_number":"101020331","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"article_type":"original","status":"public","citation":{"short":"X. Ding, H.C. Ji, Stochastic Processes and Their Applications 163 (2023) 25–60.","ieee":"X. Ding and H. C. Ji, “Spiked multiplicative random matrices and principal components,” <i>Stochastic Processes and their Applications</i>, vol. 163. Elsevier, pp. 25–60, 2023.","chicago":"Ding, Xiucai, and Hong Chang Ji. “Spiked Multiplicative Random Matrices and Principal Components.” <i>Stochastic Processes and Their Applications</i>. Elsevier, 2023. <a href=\"https://doi.org/10.1016/j.spa.2023.05.009\">https://doi.org/10.1016/j.spa.2023.05.009</a>.","apa":"Ding, X., &#38; Ji, H. C. (2023). Spiked multiplicative random matrices and principal components. <i>Stochastic Processes and Their Applications</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.spa.2023.05.009\">https://doi.org/10.1016/j.spa.2023.05.009</a>","mla":"Ding, Xiucai, and Hong Chang Ji. “Spiked Multiplicative Random Matrices and Principal Components.” <i>Stochastic Processes and Their Applications</i>, vol. 163, Elsevier, 2023, pp. 25–60, doi:<a href=\"https://doi.org/10.1016/j.spa.2023.05.009\">10.1016/j.spa.2023.05.009</a>.","ista":"Ding X, Ji HC. 2023. Spiked multiplicative random matrices and principal components. Stochastic Processes and their Applications. 163, 25–60.","ama":"Ding X, Ji HC. Spiked multiplicative random matrices and principal components. <i>Stochastic Processes and their Applications</i>. 2023;163:25-60. doi:<a href=\"https://doi.org/10.1016/j.spa.2023.05.009\">10.1016/j.spa.2023.05.009</a>"},"day":"01","file_date_updated":"2024-01-16T08:47:31Z","has_accepted_license":"1","ec_funded":1,"file":[{"relation":"main_file","success":1,"checksum":"46a708b0cd5569a73d0f3d6c3e0a44dc","date_created":"2024-01-16T08:47:31Z","date_updated":"2024-01-16T08:47:31Z","file_name":"2023_StochasticProcAppl_Ding.pdf","file_size":1870349,"creator":"dernst","access_level":"open_access","content_type":"application/pdf","file_id":"14806"}],"arxiv":1,"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","intvolume":"       163","abstract":[{"lang":"eng","text":"In this paper, we study the eigenvalues and eigenvectors of the spiked invariant multiplicative models when the randomness is from Haar matrices. We establish the limits of the outlier eigenvalues λˆi and the generalized components (⟨v,uˆi⟩ for any deterministic vector v) of the outlier eigenvectors uˆi with optimal convergence rates. Moreover, we prove that the non-outlier eigenvalues stick with those of the unspiked matrices and the non-outlier eigenvectors are delocalized. The results also hold near the so-called BBP transition and for degenerate spikes. On one hand, our results can be regarded as a refinement of the counterparts of [12] under additional regularity conditions. On the other hand, they can be viewed as an analog of [34] by replacing the random matrix with i.i.d. entries with Haar random matrix."}],"publication_status":"published","quality_controlled":"1","scopus_import":"1","oa":1,"keyword":["Applied Mathematics","Modeling and Simulation","Statistics and Probability"],"external_id":{"isi":["001113615900001"],"arxiv":["2302.13502"]},"language":[{"iso":"eng"}]},{"project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"issue":"6","type":"journal_article","publication":"The Annals of Probability","publisher":"Institute of Mathematical Statistics","isi":1,"fulldoi":"https://doi.org/10.1214/23-aop1643","date_published":"2023-11-01T00:00:00Z","article_processing_charge":"No","title":"On the rightmost eigenvalue of non-Hermitian random matrices","publication_identifier":{"issn":["0091-1798"]},"author":[{"first_name":"Giorgio","orcid":"0000-0002-4901-7992","last_name":"Cipolloni","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio"},{"full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","orcid":"0000-0001-5366-9603","first_name":"László"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","last_name":"Schröder","full_name":"Schröder, Dominik J","first_name":"Dominik J","orcid":"0000-0002-2904-1856"},{"first_name":"Yuanyuan","last_name":"Xu","full_name":"Xu, Yuanyuan"}],"date_created":"2024-01-22T08:08:41Z","department":[{"_id":"LaEr"}],"doi":"10.1214/23-aop1643","year":"2023","acknowledgement":"The second and the fourth author were supported by the ERC Advanced Grant\r\n“RMTBeyond” No. 101020331. The third author was supported by Dr. Max Rössler, the\r\nWalter Haefner Foundation and the ETH Zürich Foundation.","_id":"14849","page":"2192-2242","volume":51,"date_updated":"2025-09-09T14:23:34Z","month":"11","oa_version":"Preprint","corr_author":"1","oa":1,"external_id":{"arxiv":["2206.04448"],"isi":["001112165000004"]},"language":[{"iso":"eng"}],"keyword":["Statistics","Probability and Uncertainty","Statistics and Probability"],"scopus_import":"1","quality_controlled":"1","publication_status":"published","abstract":[{"lang":"eng","text":"We establish a precise three-term asymptotic expansion, with an optimal estimate of the error term, for the rightmost eigenvalue of an n×n random matrix with independent identically distributed complex entries as n tends to infinity. All terms in the expansion are universal."}],"intvolume":"        51","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","arxiv":1,"ec_funded":1,"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2206.04448"}],"day":"01","article_type":"original","status":"public","citation":{"mla":"Cipolloni, Giorgio, et al. “On the Rightmost Eigenvalue of Non-Hermitian Random Matrices.” <i>The Annals of Probability</i>, vol. 51, no. 6, Institute of Mathematical Statistics, 2023, pp. 2192–242, doi:<a href=\"https://doi.org/10.1214/23-aop1643\">10.1214/23-aop1643</a>.","ista":"Cipolloni G, Erdös L, Schröder DJ, Xu Y. 2023. On the rightmost eigenvalue of non-Hermitian random matrices. The Annals of Probability. 51(6), 2192–2242.","ama":"Cipolloni G, Erdös L, Schröder DJ, Xu Y. On the rightmost eigenvalue of non-Hermitian random matrices. <i>The Annals of Probability</i>. 2023;51(6):2192-2242. doi:<a href=\"https://doi.org/10.1214/23-aop1643\">10.1214/23-aop1643</a>","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Y. Xu, The Annals of Probability 51 (2023) 2192–2242.","ieee":"G. Cipolloni, L. Erdös, D. J. Schröder, and Y. Xu, “On the rightmost eigenvalue of non-Hermitian random matrices,” <i>The Annals of Probability</i>, vol. 51, no. 6. Institute of Mathematical Statistics, pp. 2192–2242, 2023.","chicago":"Cipolloni, Giorgio, László Erdös, Dominik J Schröder, and Yuanyuan Xu. “On the Rightmost Eigenvalue of Non-Hermitian Random Matrices.” <i>The Annals of Probability</i>. Institute of Mathematical Statistics, 2023. <a href=\"https://doi.org/10.1214/23-aop1643\">https://doi.org/10.1214/23-aop1643</a>.","apa":"Cipolloni, G., Erdös, L., Schröder, D. J., &#38; Xu, Y. (2023). On the rightmost eigenvalue of non-Hermitian random matrices. <i>The Annals of Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/23-aop1643\">https://doi.org/10.1214/23-aop1643</a>"}},{"intvolume":"        12","abstract":[{"lang":"eng","text":"We study moments of characteristic polynomials of truncated Haar distributed matrices from the three classical compact groups O(N), U(N) and Sp(2N). For finite matrix size we calculate the moments in terms of hypergeometric functions of matrix argument and give explicit integral representations highlighting the duality between the moment and the matrix size as well as the duality between the orthogonal and symplectic cases. Asymptotic expansions in strong and weak non-unitarity regimes are obtained. Using the connection to matrix hypergeometric functions, we establish limit theorems for the log-modulus of the characteristic polynomial evaluated on the unit circle."}],"quality_controlled":"1","scopus_import":"1","external_id":{"isi":["000848874400001"],"arxiv":["2109.10331"]},"language":[{"iso":"eng"}],"oa":1,"publication_status":"published","status":"public","citation":{"chicago":"Serebryakov, Alexander, Nick Simm, and Guillaume Dubach. “Characteristic Polynomials of Random Truncations: Moments, Duality and Asymptotics.” <i>Random Matrices: Theory and Applications</i>. World Scientific Publishing, 2023. <a href=\"https://doi.org/10.1142/s2010326322500496\">https://doi.org/10.1142/s2010326322500496</a>.","apa":"Serebryakov, A., Simm, N., &#38; Dubach, G. (2023). Characteristic polynomials of random truncations: Moments, duality and asymptotics. <i>Random Matrices: Theory and Applications</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/s2010326322500496\">https://doi.org/10.1142/s2010326322500496</a>","short":"A. Serebryakov, N. Simm, G. Dubach, Random Matrices: Theory and Applications 12 (2023).","ieee":"A. Serebryakov, N. Simm, and G. Dubach, “Characteristic polynomials of random truncations: Moments, duality and asymptotics,” <i>Random Matrices: Theory and Applications</i>, vol. 12, no. 01. World Scientific Publishing, 2023.","ista":"Serebryakov A, Simm N, Dubach G. 2023. Characteristic polynomials of random truncations: Moments, duality and asymptotics. Random Matrices: Theory and Applications. 12(01), 2250049.","ama":"Serebryakov A, Simm N, Dubach G. Characteristic polynomials of random truncations: Moments, duality and asymptotics. <i>Random Matrices: Theory and Applications</i>. 2023;12(01). doi:<a href=\"https://doi.org/10.1142/s2010326322500496\">10.1142/s2010326322500496</a>","mla":"Serebryakov, Alexander, et al. “Characteristic Polynomials of Random Truncations: Moments, Duality and Asymptotics.” <i>Random Matrices: Theory and Applications</i>, vol. 12, no. 01, 2250049, World Scientific Publishing, 2023, doi:<a href=\"https://doi.org/10.1142/s2010326322500496\">10.1142/s2010326322500496</a>."},"article_type":"original","day":"01","arxiv":1,"article_number":"2250049","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2109.10331"}],"date_published":"2023-01-01T00:00:00Z","isi":1,"fulldoi":"https://doi.org/10.1142/s2010326322500496","publisher":"World Scientific Publishing","publication_identifier":{"issn":["2010-3263"],"eissn":["2010-3271"]},"title":"Characteristic polynomials of random truncations: Moments, duality and asymptotics","article_processing_charge":"No","publication":"Random Matrices: Theory and Applications","type":"journal_article","issue":"01","volume":12,"_id":"17079","oa_version":"Preprint","date_updated":"2025-09-09T14:27:10Z","month":"01","date_created":"2024-05-29T06:14:26Z","author":[{"full_name":"Serebryakov, Alexander","last_name":"Serebryakov","first_name":"Alexander"},{"last_name":"Simm","full_name":"Simm, Nick","first_name":"Nick"},{"id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E","last_name":"Dubach","full_name":"Dubach, Guillaume","first_name":"Guillaume","orcid":"0000-0001-6892-8137"}],"acknowledgement":"N.S. gratefully acknowledges financial support of the Royal Society, grant URF/R1/180707. We would like to thank Emma Bailey, Yan Fyodorov and Jordan Stoyanov for helpful comments an an earlier version of this paper. We are grateful for the comments of an anonymous referee.","year":"2023","doi":"10.1142/s2010326322500496","department":[{"_id":"LaEr"}]},{"related_material":{"record":[{"id":"18762","relation":"later_version","status":"public"},{"id":"17164","status":"public","relation":"dissertation_contains"}]},"fulldoi":"https://doi.org/10.48550/arXiv.2307.11028","date_published":"2023-07-21T00:00:00Z","title":"Multi-point functional central limit theorem for Wigner Matrices","article_processing_charge":"No","abstract":[{"lang":"eng","text":"Consider the random variable $\\mathrm{Tr}( f_1(W)A_1\\dots f_k(W)A_k)$ where $W$ is an $N\\times N$ Hermitian Wigner matrix, $k\\in\\mathbb{N}$, and choose (possibly $N$-dependent) regular functions $f_1,\\dots, f_k$ as well as bounded deterministic matrices $A_1,\\dots,A_k$. We give a functional central limit theorem showing that the fluctuations around the expectation are Gaussian. Moreover, we determine the limiting covariance structure and give explicit error bounds in terms of the scaling of $f_1,\\dots,f_k$ and the number of traceless matrices among $A_1,\\dots,A_k$, thus extending the results of [Cipolloni, Erdős, Schröder 2023] to products of arbitrary length $k\\geq2$. As an application, we consider the fluctuation of $\\mathrm{Tr}(\\mathrm{e}^{\\mathrm{i} tW}A_1\\mathrm{e}^{-\\mathrm{i} tW}A_2)$ around its thermal value $\\mathrm{Tr}(A_1)\\mathrm{Tr}(A_2)$ when $t$ is large and give an explicit formula for the variance."}],"oa":1,"language":[{"iso":"eng"}],"external_id":{"arxiv":["2307.11028"]},"OA_place":"repository","type":"preprint","publication_status":"draft","publication":"arXiv","_id":"17173","date_updated":"2026-04-07T13:02:12Z","month":"07","oa_version":"Preprint","day":"21","citation":{"apa":"Reker, J. (n.d.). Multi-point functional central limit theorem for Wigner Matrices. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2307.11028\">https://doi.org/10.48550/arXiv.2307.11028</a>","chicago":"Reker, Jana. “Multi-Point Functional Central Limit Theorem for Wigner Matrices.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2307.11028\">https://doi.org/10.48550/arXiv.2307.11028</a>.","short":"J. Reker, ArXiv (n.d.).","ieee":"J. Reker, “Multi-point functional central limit theorem for Wigner Matrices,” <i>arXiv</i>. .","ista":"Reker J. Multi-point functional central limit theorem for Wigner Matrices. arXiv, 2307.11028.","ama":"Reker J. Multi-point functional central limit theorem for Wigner Matrices. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2307.11028\">10.48550/arXiv.2307.11028</a>","mla":"Reker, Jana. “Multi-Point Functional Central Limit Theorem for Wigner Matrices.” <i>ArXiv</i>, 2307.11028, doi:<a href=\"https://doi.org/10.48550/arXiv.2307.11028\">10.48550/arXiv.2307.11028</a>."},"status":"public","article_number":"2307.11028","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"full_name":"Reker, Jana","id":"e796e4f9-dc8d-11ea-abe3-97e26a0323e9","last_name":"Reker","first_name":"Jana"}],"date_created":"2024-06-26T08:54:56Z","arxiv":1,"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2307.11028","open_access":"1"}],"department":[{"_id":"LaEr"}],"doi":"10.48550/arXiv.2307.11028","year":"2023"},{"abstract":[{"lang":"eng","text":"We prove that a class of weakly perturbed Hamiltonians of the form $H_λ= H_0 + λW$, with $W$ being a Wigner matrix, exhibits prethermalization. That is, the time evolution generated by $H_λ$ relaxes to its ultimate thermal state via an intermediate prethermal state with a lifetime of order $λ^{-2}$. Moreover, we obtain a general relaxation formula, expressing the perturbed dynamics via the unperturbed dynamics and the ultimate thermal state. The proof relies on a two-resolvent law for the deformed Wigner matrix $H_λ$."}],"related_material":{"record":[{"status":"public","relation":"later_version","id":"18764"},{"status":"public","relation":"dissertation_contains","id":"20575"},{"relation":"dissertation_contains","status":"public","id":"17164"}]},"OA_place":"repository","publication_status":"draft","language":[{"iso":"eng"}],"external_id":{"arxiv":["2310.06677"]},"oa":1,"day":"23","status":"public","citation":{"mla":"Erdös, László, et al. “Prethermalization for Deformed Wigner Matrices.” <i>ArXiv</i>, 2310.06677, doi:<a href=\"https://doi.org/10.48550/arXiv.2310.06677\">10.48550/arXiv.2310.06677</a>.","ama":"Erdös L, Henheik SJ, Reker J, Riabov V. Prethermalization for deformed Wigner Matrices. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2310.06677\">10.48550/arXiv.2310.06677</a>","ista":"Erdös L, Henheik SJ, Reker J, Riabov V. Prethermalization for deformed Wigner Matrices. arXiv, 2310.06677.","ieee":"L. Erdös, S. J. Henheik, J. Reker, and V. Riabov, “Prethermalization for deformed Wigner Matrices,” <i>arXiv</i>. .","short":"L. Erdös, S.J. Henheik, J. Reker, V. Riabov, ArXiv (n.d.).","apa":"Erdös, L., Henheik, S. J., Reker, J., &#38; Riabov, V. (n.d.). Prethermalization for deformed Wigner Matrices. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2310.06677\">https://doi.org/10.48550/arXiv.2310.06677</a>","chicago":"Erdös, László, Sven Joscha Henheik, Jana Reker, and Volodymyr Riabov. “Prethermalization for Deformed Wigner Matrices.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2310.06677\">https://doi.org/10.48550/arXiv.2310.06677</a>."},"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2310.06677"}],"ec_funded":1,"article_number":"2310.06677","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","arxiv":1,"article_processing_charge":"No","title":"Prethermalization for deformed Wigner Matrices","date_published":"2023-12-23T00:00:00Z","fulldoi":"https://doi.org/10.48550/arXiv.2310.06677","type":"preprint","publication":"arXiv","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"month":"12","oa_version":"Preprint","date_updated":"2026-04-07T13:02:12Z","corr_author":"1","_id":"17174","doi":"10.48550/arXiv.2310.06677","department":[{"_id":"LaEr"}],"year":"2023","author":[{"orcid":"0000-0001-5366-9603","first_name":"László","full_name":"Erdös, László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Sven Joscha","orcid":"0000-0003-1106-327X","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","last_name":"Henheik","full_name":"Henheik, Sven Joscha"},{"full_name":"Reker, Jana","id":"e796e4f9-dc8d-11ea-abe3-97e26a0323e9","last_name":"Reker","first_name":"Jana"},{"last_name":"Riabov","id":"1949f904-edfb-11eb-afb5-e2dfddabb93b","full_name":"Riabov, Volodymyr","first_name":"Volodymyr"}],"date_created":"2024-06-26T08:56:52Z"},{"file_date_updated":"2023-10-04T09:21:48Z","day":"01","article_type":"original","citation":{"short":"G. Cipolloni, L. Erdös, D.J. Schröder, Communications on Pure and Applied Mathematics 76 (2023) 946–1034.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Central limit theorem for linear eigenvalue statistics of non-Hermitian random matrices,” <i>Communications on Pure and Applied Mathematics</i>, vol. 76, no. 5. Wiley, pp. 946–1034, 2023.","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2023). Central limit theorem for linear eigenvalue statistics of non-Hermitian random matrices. <i>Communications on Pure and Applied Mathematics</i>. Wiley. <a href=\"https://doi.org/10.1002/cpa.22028\">https://doi.org/10.1002/cpa.22028</a>","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Central Limit Theorem for Linear Eigenvalue Statistics of Non-Hermitian Random Matrices.” <i>Communications on Pure and Applied Mathematics</i>. Wiley, 2023. <a href=\"https://doi.org/10.1002/cpa.22028\">https://doi.org/10.1002/cpa.22028</a>.","mla":"Cipolloni, Giorgio, et al. “Central Limit Theorem for Linear Eigenvalue Statistics of Non-Hermitian Random Matrices.” <i>Communications on Pure and Applied Mathematics</i>, vol. 76, no. 5, Wiley, 2023, pp. 946–1034, doi:<a href=\"https://doi.org/10.1002/cpa.22028\">10.1002/cpa.22028</a>.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2023. Central limit theorem for linear eigenvalue statistics of non-Hermitian random matrices. Communications on Pure and Applied Mathematics. 76(5), 946–1034.","ama":"Cipolloni G, Erdös L, Schröder DJ. Central limit theorem for linear eigenvalue statistics of non-Hermitian random matrices. <i>Communications on Pure and Applied Mathematics</i>. 2023;76(5):946-1034. doi:<a href=\"https://doi.org/10.1002/cpa.22028\">10.1002/cpa.22028</a>"},"status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file":[{"date_created":"2023-10-04T09:21:48Z","checksum":"8346bc2642afb4ccb7f38979f41df5d9","success":1,"relation":"main_file","file_id":"14388","content_type":"application/pdf","access_level":"open_access","creator":"dernst","file_size":803440,"file_name":"2023_CommPureMathematics_Cipolloni.pdf","date_updated":"2023-10-04T09:21:48Z"}],"arxiv":1,"ec_funded":1,"has_accepted_license":"1","abstract":[{"text":"We consider large non-Hermitian random matrices X with complex, independent, identically distributed centred entries and show that the linear statistics of their eigenvalues are asymptotically Gaussian for test functions having 2+ϵ derivatives. Previously this result was known only for a few special cases; either the test functions were required to be analytic [72], or the distribution of the matrix elements needed to be Gaussian [73], or at least match the Gaussian up to the first four moments [82, 56]. We find the exact dependence of the limiting variance on the fourth cumulant that was not known before. The proof relies on two novel ingredients: (i) a local law for a product of two resolvents of the Hermitisation of X with different spectral parameters and (ii) a coupling of several weakly dependent Dyson Brownian motions. These methods are also the key inputs for our analogous results on the linear eigenvalue statistics of real matrices X that are presented in the companion paper [32]. ","lang":"eng"}],"intvolume":"        76","oa":1,"external_id":{"arxiv":["1912.04100"],"isi":["000724652500001"]},"language":[{"iso":"eng"}],"scopus_import":"1","quality_controlled":"1","publication_status":"published","_id":"10405","page":"946-1034","volume":76,"tmp":{"name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","short":"CC BY-NC-ND (4.0)","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","image":"/images/cc_by_nc_nd.png"},"date_updated":"2025-03-31T16:00:54Z","month":"05","oa_version":"Published Version","corr_author":"1","author":[{"first_name":"Giorgio","orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","last_name":"Cipolloni","full_name":"Cipolloni, Giorgio"},{"last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","first_name":"László","orcid":"0000-0001-5366-9603"},{"first_name":"Dominik J","orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","last_name":"Schröder","full_name":"Schröder, Dominik J"}],"date_created":"2021-12-05T23:01:41Z","department":[{"_id":"LaEr"}],"doi":"10.1002/cpa.22028","year":"2023","acknowledgement":"L.E. would like to thank Nathanaël Berestycki and D.S.would like to thank Nina Holden for valuable discussions on the Gaussian freefield.G.C. and L.E. are partially supported by ERC Advanced Grant No. 338804.G.C. received funding from the European Union’s Horizon 2020 research and in-novation programme under the Marie Skłodowska-Curie Grant Agreement No.665385. D.S. is supported by Dr. Max Rössler, the Walter Haefner Foundation, and the ETH Zürich Foundation.","ddc":["510"],"publisher":"Wiley","fulldoi":"https://doi.org/10.1002/cpa.22028","isi":1,"date_published":"2023-05-01T00:00:00Z","article_processing_charge":"Yes (via OA deal)","title":"Central limit theorem for linear eigenvalue statistics of non-Hermitian random matrices","publication_identifier":{"issn":["0010-3640"],"eissn":["1097-0312"]},"project":[{"name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"},{"name":"International IST Doctoral Program","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","grant_number":"665385","call_identifier":"H2020"}],"issue":"5","type":"journal_article","publication":"Communications on Pure and Applied Mathematics"},{"ec_funded":1,"has_accepted_license":"1","article_number":"128","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","arxiv":1,"file":[{"success":1,"relation":"main_file","checksum":"c2ef6b2aecfee1ad6d03fab620507c2c","date_created":"2023-07-31T07:49:31Z","file_name":"2023_JourStatPhysics_Sugimoto.pdf","date_updated":"2023-07-31T07:49:31Z","file_size":612755,"access_level":"open_access","creator":"dernst","file_id":"13325","content_type":"application/pdf"}],"day":"21","file_date_updated":"2023-07-31T07:49:31Z","article_type":"original","citation":{"short":"S. Sugimoto, S.J. Henheik, V. Riabov, L. Erdös, Journal of Statistical Physics 190 (2023).","ieee":"S. Sugimoto, S. J. Henheik, V. Riabov, and L. Erdös, “Eigenstate thermalisation hypothesis for translation invariant spin systems,” <i>Journal of Statistical Physics</i>, vol. 190, no. 7. Springer Nature, 2023.","apa":"Sugimoto, S., Henheik, S. J., Riabov, V., &#38; Erdös, L. (2023). Eigenstate thermalisation hypothesis for translation invariant spin systems. <i>Journal of Statistical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s10955-023-03132-4\">https://doi.org/10.1007/s10955-023-03132-4</a>","chicago":"Sugimoto, Shoki, Sven Joscha Henheik, Volodymyr Riabov, and László Erdös. “Eigenstate Thermalisation Hypothesis for Translation Invariant Spin Systems.” <i>Journal of Statistical Physics</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s10955-023-03132-4\">https://doi.org/10.1007/s10955-023-03132-4</a>.","mla":"Sugimoto, Shoki, et al. “Eigenstate Thermalisation Hypothesis for Translation Invariant Spin Systems.” <i>Journal of Statistical Physics</i>, vol. 190, no. 7, 128, Springer Nature, 2023, doi:<a href=\"https://doi.org/10.1007/s10955-023-03132-4\">10.1007/s10955-023-03132-4</a>.","ista":"Sugimoto S, Henheik SJ, Riabov V, Erdös L. 2023. Eigenstate thermalisation hypothesis for translation invariant spin systems. Journal of Statistical Physics. 190(7), 128.","ama":"Sugimoto S, Henheik SJ, Riabov V, Erdös L. Eigenstate thermalisation hypothesis for translation invariant spin systems. <i>Journal of Statistical Physics</i>. 2023;190(7). doi:<a href=\"https://doi.org/10.1007/s10955-023-03132-4\">10.1007/s10955-023-03132-4</a>"},"status":"public","publication_status":"published","oa":1,"language":[{"iso":"eng"}],"external_id":{"isi":["001035677200002"],"arxiv":["2304.04213"]},"quality_controlled":"1","scopus_import":"1","abstract":[{"lang":"eng","text":"We prove the Eigenstate Thermalisation Hypothesis (ETH) for local observables in a typical translation invariant system of quantum spins with L-body interactions, where L is the number of spins. This mathematically verifies the observation first made by Santos and Rigol (Phys Rev E 82(3):031130, 2010, https://doi.org/10.1103/PhysRevE.82.031130) that the ETH may hold for systems with additional translational symmetries for a naturally restricted class of observables. We also present numerical support for the same phenomenon for Hamiltonians with local interaction."}],"intvolume":"       190","related_material":{"record":[{"id":"20575","relation":"dissertation_contains","status":"public"},{"status":"public","relation":"dissertation_contains","id":"19540"}]},"department":[{"_id":"LaEr"}],"doi":"10.1007/s10955-023-03132-4","year":"2023","acknowledgement":"LE, JH, and VR were supported by ERC Advanced Grant “RMTBeyond” No. 101020331. SS was supported by KAKENHI Grant Number JP22J14935 from the Japan Society for the Promotion of Science (JSPS) and Forefront Physics and Mathematics Program to Drive Transformation (FoPM), a World-leading Innovative Graduate Study (WINGS) Program, the University of Tokyo.\r\nOpen access funding provided by The University of Tokyo.","author":[{"first_name":"Shoki","full_name":"Sugimoto, Shoki","last_name":"Sugimoto"},{"first_name":"Sven Joscha","orcid":"0000-0003-1106-327X","last_name":"Henheik","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","full_name":"Henheik, Sven Joscha"},{"last_name":"Riabov","id":"1949f904-edfb-11eb-afb5-e2dfddabb93b","full_name":"Riabov, Volodymyr","first_name":"Volodymyr"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","full_name":"Erdös, László","first_name":"László","orcid":"0000-0001-5366-9603"}],"date_created":"2023-07-30T22:01:02Z","tmp":{"short":"CC BY (4.0)","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)"},"date_updated":"2026-07-29T13:18:16Z","oa_version":"Published Version","month":"07","_id":"13317","volume":190,"issue":"7","type":"journal_article","publication":"Journal of Statistical Physics","project":[{"call_identifier":"H2020","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"article_processing_charge":"Yes (in subscription journal)","title":"Eigenstate thermalisation hypothesis for translation invariant spin systems","publication_identifier":{"eissn":["1572-9613"],"issn":["0022-4715"]},"publisher":"Springer Nature","ddc":["510","530"],"isi":1,"fulldoi":"https://doi.org/10.1007/s10955-023-03132-4","date_published":"2023-07-21T00:00:00Z"},{"month":"08","tmp":{"short":"CC BY (4.0)","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)"},"oa_version":"Published Version","date_updated":"2026-07-29T13:18:16Z","corr_author":"1","_id":"14343","volume":11,"doi":"10.1017/fms.2023.70","department":[{"_id":"LaEr"},{"_id":"GradSch"}],"acknowledgement":"G.C. and L.E. gratefully acknowledge many discussions with Dominik Schröder at the preliminary stage of this project, especially his essential contribution to identify the correct generalisation of traceless observables to the deformed Wigner ensembles.\r\nL.E. and J.H. acknowledges support by ERC Advanced Grant ‘RMTBeyond’ No. 101020331.","year":"2023","author":[{"first_name":"Giorgio","orcid":"0000-0002-4901-7992","last_name":"Cipolloni","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio"},{"orcid":"0000-0001-5366-9603","first_name":"László","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös"},{"full_name":"Henheik, Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","last_name":"Henheik","orcid":"0000-0003-1106-327X","first_name":"Sven Joscha"},{"first_name":"Oleksii","orcid":"0000-0003-1491-4623","last_name":"Kolupaiev","id":"149b70d4-896a-11ed-bdf8-8c63fd44ca61","full_name":"Kolupaiev, Oleksii"}],"date_created":"2023-09-17T22:01:09Z","publication_identifier":{"eissn":["2050-5094"]},"title":"Gaussian fluctuations in the equipartition principle for Wigner matrices","article_processing_charge":"Yes","ddc":["510"],"publisher":"Cambridge University Press","date_published":"2023-08-23T00:00:00Z","fulldoi":"https://doi.org/10.1017/fms.2023.70","isi":1,"type":"journal_article","publication":"Forum of Mathematics, Sigma","project":[{"call_identifier":"H2020","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"file_date_updated":"2023-09-20T11:09:35Z","day":"23","citation":{"ama":"Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. Gaussian fluctuations in the equipartition principle for Wigner matrices. <i>Forum of Mathematics, Sigma</i>. 2023;11. doi:<a href=\"https://doi.org/10.1017/fms.2023.70\">10.1017/fms.2023.70</a>","ista":"Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. 2023. Gaussian fluctuations in the equipartition principle for Wigner matrices. Forum of Mathematics, Sigma. 11, e74.","mla":"Cipolloni, Giorgio, et al. “Gaussian Fluctuations in the Equipartition Principle for Wigner Matrices.” <i>Forum of Mathematics, Sigma</i>, vol. 11, e74, Cambridge University Press, 2023, doi:<a href=\"https://doi.org/10.1017/fms.2023.70\">10.1017/fms.2023.70</a>.","chicago":"Cipolloni, Giorgio, László Erdös, Sven Joscha Henheik, and Oleksii Kolupaiev. “Gaussian Fluctuations in the Equipartition Principle for Wigner Matrices.” <i>Forum of Mathematics, Sigma</i>. Cambridge University Press, 2023. <a href=\"https://doi.org/10.1017/fms.2023.70\">https://doi.org/10.1017/fms.2023.70</a>.","apa":"Cipolloni, G., Erdös, L., Henheik, S. J., &#38; Kolupaiev, O. (2023). Gaussian fluctuations in the equipartition principle for Wigner matrices. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fms.2023.70\">https://doi.org/10.1017/fms.2023.70</a>","ieee":"G. Cipolloni, L. Erdös, S. J. Henheik, and O. Kolupaiev, “Gaussian fluctuations in the equipartition principle for Wigner matrices,” <i>Forum of Mathematics, Sigma</i>, vol. 11. Cambridge University Press, 2023.","short":"G. Cipolloni, L. Erdös, S.J. Henheik, O. Kolupaiev, Forum of Mathematics, Sigma 11 (2023)."},"status":"public","article_type":"original","ec_funded":1,"has_accepted_license":"1","article_number":"e74","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","file":[{"relation":"main_file","success":1,"date_created":"2023-09-20T11:09:35Z","checksum":"eb747420e6a88a7796fa934151957676","file_size":852652,"date_updated":"2023-09-20T11:09:35Z","file_name":"2023_ForumMathematics_Cipolloni.pdf","file_id":"14352","content_type":"application/pdf","creator":"dernst","access_level":"open_access"}],"arxiv":1,"abstract":[{"lang":"eng","text":"The total energy of an eigenstate in a composite quantum system tends to be distributed equally among its constituents. We identify the quantum fluctuation around this equipartition principle in the simplest disordered quantum system consisting of linear combinations of Wigner matrices. As our main ingredient, we prove the Eigenstate Thermalisation Hypothesis and Gaussian fluctuation for general quadratic forms of the bulk eigenvectors of Wigner matrices with an arbitrary deformation."}],"intvolume":"        11","related_material":{"record":[{"id":"19540","relation":"dissertation_contains","status":"public"}]},"publication_status":"published","external_id":{"isi":["001051980200001"],"arxiv":["2301.05181"]},"language":[{"iso":"eng"}],"oa":1,"quality_controlled":"1","scopus_import":"1"},{"date_published":"2023-10-11T00:00:00Z","isi":1,"fulldoi":"https://doi.org/10.1088/1751-8121/acfe62","publisher":"IOP Publishing","ddc":["510"],"publication_identifier":{"eissn":["1751-8121"],"issn":["1751-8113"]},"title":"Creation rate of Dirac particles at a point source","article_processing_charge":"Yes (via OA deal)","project":[{"grant_number":"101020331","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"publication":"Journal of Physics A: Mathematical and Theoretical","type":"journal_article","issue":"44","volume":56,"_id":"14421","corr_author":"1","tmp":{"short":"CC BY (4.0)","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)"},"month":"10","oa_version":"Published Version","date_updated":"2026-07-29T13:18:16Z","date_created":"2023-10-12T12:42:53Z","author":[{"orcid":"0000-0003-1106-327X","first_name":"Sven Joscha","full_name":"Henheik, Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","last_name":"Henheik"},{"first_name":"Roderich","last_name":"Tumulka","full_name":"Tumulka, Roderich"}],"acknowledgement":"J H gratefully acknowledges partial financial support by the ERC Advanced Grant 'RMTBeyond' No. 101020331.","year":"2023","doi":"10.1088/1751-8121/acfe62","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"related_material":{"record":[{"id":"19540","relation":"dissertation_contains","status":"public"}]},"intvolume":"        56","abstract":[{"lang":"eng","text":"Only recently has it been possible to construct a self-adjoint Hamiltonian that involves the creation of Dirac particles at a point source in 3d space. Its definition makes use of an interior-boundary condition. Here, we develop for this Hamiltonian a corresponding theory of the Bohmian configuration. That is, we (non-rigorously) construct a Markov jump process $(Q_t)_{t\\in\\mathbb{R}}$ in the configuration space of a variable number of particles that is $|\\psi_t|^2$-distributed at every time t and follows Bohmian trajectories between the jumps. The jumps correspond to particle creation or annihilation events and occur either to or from a configuration with a particle located at the source. The process is the natural analog of Bell's jump process, and a central piece in its construction is the determination of the rate of particle creation. The construction requires an analysis of the asymptotic behavior of the Bohmian trajectories near the source. We find that the particle reaches the source with radial speed 0, but orbits around the source infinitely many times in finite time before absorption (or after emission)."}],"scopus_import":"1","quality_controlled":"1","external_id":{"isi":["001080908000001"],"arxiv":["2211.16606"]},"language":[{"iso":"eng"}],"oa":1,"publication_status":"published","status":"public","citation":{"ieee":"S. J. Henheik and R. Tumulka, “Creation rate of Dirac particles at a point source,” <i>Journal of Physics A: Mathematical and Theoretical</i>, vol. 56, no. 44. IOP Publishing, 2023.","short":"S.J. Henheik, R. Tumulka, Journal of Physics A: Mathematical and Theoretical 56 (2023).","chicago":"Henheik, Sven Joscha, and Roderich Tumulka. “Creation Rate of Dirac Particles at a Point Source.” <i>Journal of Physics A: Mathematical and Theoretical</i>. IOP Publishing, 2023. <a href=\"https://doi.org/10.1088/1751-8121/acfe62\">https://doi.org/10.1088/1751-8121/acfe62</a>.","apa":"Henheik, S. J., &#38; Tumulka, R. (2023). Creation rate of Dirac particles at a point source. <i>Journal of Physics A: Mathematical and Theoretical</i>. IOP Publishing. <a href=\"https://doi.org/10.1088/1751-8121/acfe62\">https://doi.org/10.1088/1751-8121/acfe62</a>","mla":"Henheik, Sven Joscha, and Roderich Tumulka. “Creation Rate of Dirac Particles at a Point Source.” <i>Journal of Physics A: Mathematical and Theoretical</i>, vol. 56, no. 44, 445201, IOP Publishing, 2023, doi:<a href=\"https://doi.org/10.1088/1751-8121/acfe62\">10.1088/1751-8121/acfe62</a>.","ama":"Henheik SJ, Tumulka R. Creation rate of Dirac particles at a point source. <i>Journal of Physics A: Mathematical and Theoretical</i>. 2023;56(44). doi:<a href=\"https://doi.org/10.1088/1751-8121/acfe62\">10.1088/1751-8121/acfe62</a>","ista":"Henheik SJ, Tumulka R. 2023. Creation rate of Dirac particles at a point source. Journal of Physics A: Mathematical and Theoretical. 56(44), 445201."},"article_type":"original","day":"11","file_date_updated":"2023-10-16T07:07:24Z","arxiv":1,"file":[{"content_type":"application/pdf","file_id":"14429","access_level":"open_access","creator":"dernst","file_size":721399,"date_updated":"2023-10-16T07:07:24Z","file_name":"2023_JourPhysics_Henheik.pdf","date_created":"2023-10-16T07:07:24Z","checksum":"5b68de147dd4c608b71a6e0e844d2ce9","relation":"main_file","success":1}],"article_number":"445201","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","has_accepted_license":"1","ec_funded":1},{"citation":{"ista":"Reker J. 2022. On the operator norm of a Hermitian random matrix with correlated entries. Random Matrices: Theory and Applications. 11(4), 2250036.","ama":"Reker J. On the operator norm of a Hermitian random matrix with correlated entries. <i>Random Matrices: Theory and Applications</i>. 2022;11(4). doi:<a href=\"https://doi.org/10.1142/s2010326322500368\">10.1142/s2010326322500368</a>","mla":"Reker, Jana. “On the Operator Norm of a Hermitian Random Matrix with Correlated Entries.” <i>Random Matrices: Theory and Applications</i>, vol. 11, no. 4, 2250036, World Scientific Publishing, 2022, doi:<a href=\"https://doi.org/10.1142/s2010326322500368\">10.1142/s2010326322500368</a>.","apa":"Reker, J. (2022). On the operator norm of a Hermitian random matrix with correlated entries. <i>Random Matrices: Theory and Applications</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/s2010326322500368\">https://doi.org/10.1142/s2010326322500368</a>","chicago":"Reker, Jana. “On the Operator Norm of a Hermitian Random Matrix with Correlated Entries.” <i>Random Matrices: Theory and Applications</i>. World Scientific Publishing, 2022. <a href=\"https://doi.org/10.1142/s2010326322500368\">https://doi.org/10.1142/s2010326322500368</a>.","short":"J. Reker, Random Matrices: Theory and Applications 11 (2022).","ieee":"J. Reker, “On the operator norm of a Hermitian random matrix with correlated entries,” <i>Random Matrices: Theory and Applications</i>, vol. 11, no. 4. World Scientific Publishing, 2022."},"status":"public","article_type":"original","day":"01","arxiv":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_number":"2250036","main_file_link":[{"url":" https://doi.org/10.48550/arXiv.2103.03906","open_access":"1"}],"related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"17164"}]},"intvolume":"        11","abstract":[{"text":"We consider a correlated NxN Hermitian random matrix with a polynomially decaying metric correlation structure. By calculating the trace of the moments of the matrix and using the summable decay of the cumulants, we show that its operator norm is stochastically dominated by one.","lang":"eng"}],"scopus_import":"1","quality_controlled":"1","external_id":{"arxiv":["2103.03906"],"isi":["000848873800001"]},"keyword":["Discrete Mathematics and Combinatorics","Statistics","Probability and Uncertainty","Statistics and Probability","Algebra and Number Theory"],"language":[{"iso":"eng"}],"oa":1,"publication_status":"published","volume":11,"_id":"11135","corr_author":"1","oa_version":"Preprint","month":"10","date_updated":"2026-04-07T13:02:12Z","date_created":"2022-04-08T07:11:12Z","author":[{"first_name":"Jana","id":"e796e4f9-dc8d-11ea-abe3-97e26a0323e9","last_name":"Reker","full_name":"Reker, Jana"}],"year":"2022","doi":"10.1142/s2010326322500368","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"date_published":"2022-10-01T00:00:00Z","fulldoi":"https://doi.org/10.1142/s2010326322500368","isi":1,"publisher":"World Scientific Publishing","publication_identifier":{"issn":["2010-3263"],"eissn":["2010-3271"]},"article_processing_charge":"No","title":"On the operator norm of a Hermitian random matrix with correlated entries","publication":"Random Matrices: Theory and Applications","type":"journal_article","issue":"4"},{"publication":"Communications in Mathematical Physics","type":"journal_article","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"title":"Convergence rate to the Tracy–Widom laws for the largest Eigenvalue of Wigner matrices","article_processing_charge":"No","date_published":"2022-07-01T00:00:00Z","fulldoi":"https://doi.org/10.1007/s00220-022-04377-y","isi":1,"ddc":["510"],"publisher":"Springer Nature","acknowledgement":"Kevin Schnelli is supported in parts by the Swedish Research Council Grant VR-2017-05195, and the Knut and Alice Wallenberg Foundation. Yuanyuan Xu is supported by the Swedish Research Council Grant VR-2017-05195 and the ERC Advanced Grant “RMTBeyond” No. 101020331.","year":"2022","doi":"10.1007/s00220-022-04377-y","department":[{"_id":"LaEr"}],"date_created":"2022-04-24T22:01:44Z","author":[{"orcid":"0000-0003-0954-3231","first_name":"Kevin","full_name":"Schnelli, Kevin","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","last_name":"Schnelli"},{"first_name":"Yuanyuan","orcid":"0000-0003-1559-1205","last_name":"Xu","id":"7902bdb1-a2a4-11eb-a164-c9216f71aea3","full_name":"Xu, Yuanyuan"}],"oa_version":"Published Version","tmp":{"short":"CC BY (4.0)","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)"},"month":"07","date_updated":"2025-06-11T14:01:05Z","page":"839-907","volume":393,"_id":"11332","publication_status":"published","scopus_import":"1","quality_controlled":"1","external_id":{"arxiv":["2102.04330"],"isi":["000782737200001"],"pmid":["35765414"]},"language":[{"iso":"eng"}],"oa":1,"intvolume":"       393","abstract":[{"lang":"eng","text":"We show that the fluctuations of the largest eigenvalue of a real symmetric or complex Hermitian Wigner matrix of size N converge to the Tracy–Widom laws at a rate O(N^{-1/3+\\omega }), as N tends to infinity. For Wigner matrices this improves the previous rate O(N^{-2/9+\\omega }) obtained by Bourgade (J Eur Math Soc, 2021) for generalized Wigner matrices. Our result follows from a Green function comparison theorem, originally introduced by Erdős et al. (Adv Math 229(3):1435–1515, 2012) to prove edge universality, on a finer spectral parameter scale with improved error estimates. The proof relies on the continuous Green function flow induced by a matrix-valued Ornstein–Uhlenbeck process. Precise estimates on leading contributions from the third and fourth order moments of the matrix entries are obtained using iterative cumulant expansions and recursive comparisons for correlation functions, along with uniform convergence estimates for correlation kernels of the Gaussian invariant ensembles."}],"has_accepted_license":"1","ec_funded":1,"file":[{"checksum":"bee0278c5efa9a33d9a2dc8d354a6c51","date_created":"2022-08-05T06:01:13Z","success":1,"relation":"main_file","creator":"dernst","access_level":"open_access","content_type":"application/pdf","file_id":"11726","file_name":"2022_CommunMathPhys_Schnelli.pdf","date_updated":"2022-08-05T06:01:13Z","file_size":1141462}],"arxiv":1,"pmid":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","citation":{"ama":"Schnelli K, Xu Y. Convergence rate to the Tracy–Widom laws for the largest Eigenvalue of Wigner matrices. <i>Communications in Mathematical Physics</i>. 2022;393:839-907. doi:<a href=\"https://doi.org/10.1007/s00220-022-04377-y\">10.1007/s00220-022-04377-y</a>","ista":"Schnelli K, Xu Y. 2022. Convergence rate to the Tracy–Widom laws for the largest Eigenvalue of Wigner matrices. Communications in Mathematical Physics. 393, 839–907.","mla":"Schnelli, Kevin, and Yuanyuan Xu. “Convergence Rate to the Tracy–Widom Laws for the Largest Eigenvalue of Wigner Matrices.” <i>Communications in Mathematical Physics</i>, vol. 393, Springer Nature, 2022, pp. 839–907, doi:<a href=\"https://doi.org/10.1007/s00220-022-04377-y\">10.1007/s00220-022-04377-y</a>.","apa":"Schnelli, K., &#38; Xu, Y. (2022). Convergence rate to the Tracy–Widom laws for the largest Eigenvalue of Wigner matrices. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-022-04377-y\">https://doi.org/10.1007/s00220-022-04377-y</a>","chicago":"Schnelli, Kevin, and Yuanyuan Xu. “Convergence Rate to the Tracy–Widom Laws for the Largest Eigenvalue of Wigner Matrices.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s00220-022-04377-y\">https://doi.org/10.1007/s00220-022-04377-y</a>.","ieee":"K. Schnelli and Y. Xu, “Convergence rate to the Tracy–Widom laws for the largest Eigenvalue of Wigner matrices,” <i>Communications in Mathematical Physics</i>, vol. 393. Springer Nature, pp. 839–907, 2022.","short":"K. Schnelli, Y. Xu, Communications in Mathematical Physics 393 (2022) 839–907."},"article_type":"original","file_date_updated":"2022-08-05T06:01:13Z","day":"01"},{"main_file_link":[{"url":"https://arxiv.org/abs/2103.06730","open_access":"1"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","arxiv":1,"day":"01","citation":{"short":"G. Cipolloni, L. Erdös, D.J. Schröder, Annals of Probability 50 (2022) 984–1012.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Normal fluctuation in quantum ergodicity for Wigner matrices,” <i>Annals of Probability</i>, vol. 50, no. 3. Institute of Mathematical Statistics, pp. 984–1012, 2022.","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2022). Normal fluctuation in quantum ergodicity for Wigner matrices. <i>Annals of Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/21-AOP1552\">https://doi.org/10.1214/21-AOP1552</a>","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Normal Fluctuation in Quantum Ergodicity for Wigner Matrices.” <i>Annals of Probability</i>. Institute of Mathematical Statistics, 2022. <a href=\"https://doi.org/10.1214/21-AOP1552\">https://doi.org/10.1214/21-AOP1552</a>.","mla":"Cipolloni, Giorgio, et al. “Normal Fluctuation in Quantum Ergodicity for Wigner Matrices.” <i>Annals of Probability</i>, vol. 50, no. 3, Institute of Mathematical Statistics, 2022, pp. 984–1012, doi:<a href=\"https://doi.org/10.1214/21-AOP1552\">10.1214/21-AOP1552</a>.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Normal fluctuation in quantum ergodicity for Wigner matrices. Annals of Probability. 50(3), 984–1012.","ama":"Cipolloni G, Erdös L, Schröder DJ. Normal fluctuation in quantum ergodicity for Wigner matrices. <i>Annals of Probability</i>. 2022;50(3):984-1012. doi:<a href=\"https://doi.org/10.1214/21-AOP1552\">10.1214/21-AOP1552</a>"},"status":"public","article_type":"original","publication_status":"published","language":[{"iso":"eng"}],"external_id":{"arxiv":["2103.06730"],"isi":["000793963400005"]},"oa":1,"scopus_import":"1","quality_controlled":"1","abstract":[{"text":"We consider the quadratic form of a general high-rank deterministic matrix on the eigenvectors of an N×N\r\nWigner matrix and prove that it has Gaussian fluctuation for each bulk eigenvector in the large N limit. The proof is a combination of the energy method for the Dyson Brownian motion inspired by Marcinek and Yau (2021) and our recent multiresolvent local laws (Comm. Math. Phys. 388 (2021) 1005–1048).","lang":"eng"}],"intvolume":"        50","doi":"10.1214/21-AOP1552","department":[{"_id":"LaEr"}],"acknowledgement":"L.E. would like to thank Zhigang Bao for many illuminating discussions in an early stage of this research. The authors are also grateful to Paul Bourgade for his comments on the manuscript and the anonymous referee for several useful suggestions.","year":"2022","author":[{"orcid":"0000-0002-4901-7992","first_name":"Giorgio","full_name":"Cipolloni, Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","last_name":"Cipolloni"},{"first_name":"László","orcid":"0000-0001-5366-9603","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László"},{"full_name":"Schröder, Dominik J","last_name":"Schröder","id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856","first_name":"Dominik J"}],"date_created":"2022-05-29T22:01:53Z","date_updated":"2023-08-03T07:16:53Z","oa_version":"Preprint","month":"05","_id":"11418","page":"984-1012","volume":50,"type":"journal_article","issue":"3","publication":"Annals of Probability","publication_identifier":{"issn":["0091-1798"],"eissn":["2168-894X"]},"title":"Normal fluctuation in quantum ergodicity for Wigner matrices","article_processing_charge":"No","publisher":"Institute of Mathematical Statistics","date_published":"2022-05-01T00:00:00Z","fulldoi":"https://doi.org/10.1214/21-AOP1552","isi":1},{"article_processing_charge":"No","title":"Interior-boundary conditions for the Dirac equation at point sources in three dimensions","publication_identifier":{"issn":["0022-2488"]},"fulldoi":"https://doi.org/10.1063/5.0104675","isi":1,"date_published":"2022-12-01T00:00:00Z","publisher":"AIP Publishing","ddc":["510"],"publication":"Journal of Mathematical Physics","issue":"12","type":"journal_article","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"corr_author":"1","tmp":{"short":"CC BY (4.0)","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)"},"date_updated":"2025-04-14T07:57:18Z","month":"12","oa_version":"Published Version","volume":63,"_id":"12110","year":"2022","acknowledgement":"J.H. gratefully acknowledges the partial financial support by the ERC Advanced Grant “RMTBeyond” under Grant No. 101020331.\r\n","department":[{"_id":"LaEr"}],"doi":"10.1063/5.0104675","date_created":"2023-01-08T23:00:53Z","author":[{"orcid":"0000-0003-1106-327X","first_name":"Sven Joscha","full_name":"Henheik, Sven Joscha","last_name":"Henheik","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb"},{"first_name":"Roderich","full_name":"Tumulka, Roderich","last_name":"Tumulka"}],"intvolume":"        63","abstract":[{"text":"A recently proposed approach for avoiding the ultraviolet divergence of Hamiltonians with particle creation is based on interior-boundary conditions (IBCs). The approach works well in the non-relativistic case, i.e., for the Laplacian operator. Here, we study how the approach can be applied to Dirac operators. While this has successfully been done already in one space dimension, and more generally for codimension-1 boundaries, the situation of point sources in three dimensions corresponds to a codimension-3 boundary. One would expect that, for such a boundary, Dirac operators do not allow for boundary conditions because they are known not to allow for point interactions in 3D, which also correspond to a boundary condition. Indeed, we confirm this expectation here by proving that there is no self-adjoint operator on a (truncated) Fock space that would correspond to a Dirac operator with an IBC at configurations with a particle at the origin. However, we also present a positive result showing that there are self-adjoint operators with an IBC (on the boundary consisting of configurations with a particle at the origin) that are away from those configurations, given by a Dirac operator plus a sufficiently strong Coulomb potential.","lang":"eng"}],"publication_status":"published","quality_controlled":"1","scopus_import":"1","oa":1,"external_id":{"isi":["000900748900002"]},"language":[{"iso":"eng"}],"article_type":"original","status":"public","citation":{"ieee":"S. J. Henheik and R. Tumulka, “Interior-boundary conditions for the Dirac equation at point sources in three dimensions,” <i>Journal of Mathematical Physics</i>, vol. 63, no. 12. AIP Publishing, 2022.","short":"S.J. Henheik, R. Tumulka, Journal of Mathematical Physics 63 (2022).","apa":"Henheik, S. J., &#38; Tumulka, R. (2022). Interior-boundary conditions for the Dirac equation at point sources in three dimensions. <i>Journal of Mathematical Physics</i>. AIP Publishing. <a href=\"https://doi.org/10.1063/5.0104675\">https://doi.org/10.1063/5.0104675</a>","chicago":"Henheik, Sven Joscha, and Roderich Tumulka. “Interior-Boundary Conditions for the Dirac Equation at Point Sources in Three Dimensions.” <i>Journal of Mathematical Physics</i>. AIP Publishing, 2022. <a href=\"https://doi.org/10.1063/5.0104675\">https://doi.org/10.1063/5.0104675</a>.","mla":"Henheik, Sven Joscha, and Roderich Tumulka. “Interior-Boundary Conditions for the Dirac Equation at Point Sources in Three Dimensions.” <i>Journal of Mathematical Physics</i>, vol. 63, no. 12, 122302, AIP Publishing, 2022, doi:<a href=\"https://doi.org/10.1063/5.0104675\">10.1063/5.0104675</a>.","ama":"Henheik SJ, Tumulka R. Interior-boundary conditions for the Dirac equation at point sources in three dimensions. <i>Journal of Mathematical Physics</i>. 2022;63(12). doi:<a href=\"https://doi.org/10.1063/5.0104675\">10.1063/5.0104675</a>","ista":"Henheik SJ, Tumulka R. 2022. Interior-boundary conditions for the Dirac equation at point sources in three dimensions. Journal of Mathematical Physics. 63(12), 122302."},"file_date_updated":"2023-01-20T11:58:59Z","day":"01","has_accepted_license":"1","ec_funded":1,"file":[{"date_updated":"2023-01-20T11:58:59Z","file_name":"2022_JourMathPhysics_Henheik.pdf","file_size":5436804,"creator":"dernst","access_level":"open_access","file_id":"12327","content_type":"application/pdf","relation":"main_file","success":1,"checksum":"5150287295e0ce4f12462c990744d65d","date_created":"2023-01-20T11:58:59Z"}],"article_number":"122302","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8"},{"abstract":[{"text":"We prove a general local law for Wigner matrices that optimally handles observables of arbitrary rank and thus unifies the well-known averaged and isotropic local laws. As an application, we prove a central limit theorem in quantum unique ergodicity (QUE): that is, we show that the quadratic forms of a general deterministic matrix A on the bulk eigenvectors of a Wigner matrix have approximately Gaussian fluctuation. For the bulk spectrum, we thus generalise our previous result [17] as valid for test matrices A of large rank as well as the result of Benigni and Lopatto [7] as valid for specific small-rank observables.","lang":"eng"}],"intvolume":"        10","publication_status":"published","oa":1,"external_id":{"isi":["000873719200001"]},"keyword":["Computational Mathematics","Discrete Mathematics and Combinatorics","Geometry and Topology","Mathematical Physics","Statistics and Probability","Algebra and Number Theory","Theoretical Computer Science","Analysis"],"language":[{"iso":"eng"}],"quality_controlled":"1","scopus_import":"1","day":"27","file_date_updated":"2023-01-24T10:02:40Z","article_type":"original","status":"public","citation":{"ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Rank-uniform local law for Wigner matrices,” <i>Forum of Mathematics, Sigma</i>, vol. 10. Cambridge University Press, 2022.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Forum of Mathematics, Sigma 10 (2022).","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Rank-Uniform Local Law for Wigner Matrices.” <i>Forum of Mathematics, Sigma</i>. Cambridge University Press, 2022. <a href=\"https://doi.org/10.1017/fms.2022.86\">https://doi.org/10.1017/fms.2022.86</a>.","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2022). Rank-uniform local law for Wigner matrices. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fms.2022.86\">https://doi.org/10.1017/fms.2022.86</a>","mla":"Cipolloni, Giorgio, et al. “Rank-Uniform Local Law for Wigner Matrices.” <i>Forum of Mathematics, Sigma</i>, vol. 10, e96, Cambridge University Press, 2022, doi:<a href=\"https://doi.org/10.1017/fms.2022.86\">10.1017/fms.2022.86</a>.","ama":"Cipolloni G, Erdös L, Schröder DJ. Rank-uniform local law for Wigner matrices. <i>Forum of Mathematics, Sigma</i>. 2022;10. doi:<a href=\"https://doi.org/10.1017/fms.2022.86\">10.1017/fms.2022.86</a>","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Rank-uniform local law for Wigner matrices. Forum of Mathematics, Sigma. 10, e96."},"ec_funded":1,"has_accepted_license":"1","article_number":"e96","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","file":[{"relation":"main_file","success":1,"date_created":"2023-01-24T10:02:40Z","checksum":"94a049aeb1eea5497aa097712a73c400","file_size":817089,"date_updated":"2023-01-24T10:02:40Z","file_name":"2022_ForumMath_Cipolloni.pdf","file_id":"12356","content_type":"application/pdf","access_level":"open_access","creator":"dernst"}],"article_processing_charge":"No","title":"Rank-uniform local law for Wigner matrices","publication_identifier":{"issn":["2050-5094"]},"publisher":"Cambridge University Press","ddc":["510"],"fulldoi":"https://doi.org/10.1017/fms.2022.86","isi":1,"date_published":"2022-10-27T00:00:00Z","type":"journal_article","publication":"Forum of Mathematics, Sigma","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"tmp":{"short":"CC BY (4.0)","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)"},"date_updated":"2025-04-14T07:57:18Z","month":"10","oa_version":"Published Version","corr_author":"1","_id":"12148","volume":10,"department":[{"_id":"LaEr"}],"doi":"10.1017/fms.2022.86","year":"2022","acknowledgement":"L.E. acknowledges support by ERC Advanced Grant ‘RMTBeyond’ No. 101020331. D.S. acknowledges the support of Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zürich Foundation.","author":[{"first_name":"Giorgio","orcid":"0000-0002-4901-7992","last_name":"Cipolloni","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","full_name":"Erdös, László","first_name":"László","orcid":"0000-0001-5366-9603"},{"first_name":"Dominik J","orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","last_name":"Schröder","full_name":"Schröder, Dominik J"}],"date_created":"2023-01-12T12:07:30Z"}]