[{"project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331"}],"language":[{"iso":"eng"}],"issue":"1B","publication_identifier":{"issn":["1050-5164"]},"quality_controlled":"1","doi":"10.1214/23-AAP2000","department":[{"_id":"LaEr"}],"publisher":"Institute of Mathematical Statistics","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","scopus_import":"1","ec_funded":1,"article_processing_charge":"No","article_type":"original","publication":"Annals of Applied Probability","day":"01","author":[{"first_name":"László","last_name":"Erdös","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"last_name":"McKenna","first_name":"Benjamin","id":"b0cc634c-d549-11ee-96c8-87338c7ad808","orcid":"0000-0003-2625-495X","full_name":"McKenna, Benjamin"}],"title":"Extremal statistics of quadratic forms of GOE/GUE eigenvectors","arxiv":1,"status":"public","external_id":{"arxiv":["2208.12206"]},"citation":{"ieee":"L. Erdös and B. McKenna, “Extremal statistics of quadratic forms of GOE/GUE eigenvectors,” <i>Annals of Applied Probability</i>, vol. 34, no. 1B. Institute of Mathematical Statistics, pp. 1623–1662, 2024.","chicago":"Erdös, László, and Benjamin McKenna. “Extremal Statistics of Quadratic Forms of GOE/GUE Eigenvectors.” <i>Annals of Applied Probability</i>. Institute of Mathematical Statistics, 2024. <a href=\"https://doi.org/10.1214/23-AAP2000\">https://doi.org/10.1214/23-AAP2000</a>.","short":"L. Erdös, B. McKenna, Annals of Applied Probability 34 (2024) 1623–1662.","ama":"Erdös L, McKenna B. Extremal statistics of quadratic forms of GOE/GUE eigenvectors. <i>Annals of Applied Probability</i>. 2024;34(1B):1623-1662. doi:<a href=\"https://doi.org/10.1214/23-AAP2000\">10.1214/23-AAP2000</a>","ista":"Erdös L, McKenna B. 2024. Extremal statistics of quadratic forms of GOE/GUE eigenvectors. Annals of Applied Probability. 34(1B), 1623–1662.","mla":"Erdös, László, and Benjamin McKenna. “Extremal Statistics of Quadratic Forms of GOE/GUE Eigenvectors.” <i>Annals of Applied Probability</i>, vol. 34, no. 1B, Institute of Mathematical Statistics, 2024, pp. 1623–62, doi:<a href=\"https://doi.org/10.1214/23-AAP2000\">10.1214/23-AAP2000</a>.","apa":"Erdös, L., &#38; McKenna, B. (2024). Extremal statistics of quadratic forms of GOE/GUE eigenvectors. <i>Annals of Applied Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/23-AAP2000\">https://doi.org/10.1214/23-AAP2000</a>"},"intvolume":"        34","oa":1,"publication_status":"published","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2208.12206","open_access":"1"}],"date_published":"2024-02-01T00:00:00Z","year":"2024","acknowledgement":"The first author was supported by the ERC Advanced Grant “RMTBeyond” No. 101020331. The second author was supported by Fulbright Austria and the Austrian Marshall Plan Foundation.","_id":"15025","date_updated":"2024-02-27T08:29:05Z","abstract":[{"text":"We consider quadratic forms of deterministic matrices A evaluated at the random eigenvectors of a large N×N GOE or GUE matrix, or equivalently evaluated at the columns of a Haar-orthogonal or Haar-unitary random matrix. We prove that, as long as the deterministic matrix has rank much smaller than √N, the distributions of the extrema of these quadratic forms are asymptotically the same as if the eigenvectors were independent Gaussians. This reduces the problem to Gaussian computations, which we carry out in several cases to illustrate our result, finding Gumbel or Weibull limiting distributions depending on the signature of A. Our result also naturally applies to the eigenvectors of any invariant ensemble.","lang":"eng"}],"type":"journal_article","month":"02","oa_version":"Preprint","page":"1623-1662","date_created":"2024-02-25T23:00:56Z","volume":34},{"language":[{"iso":"eng"}],"isi":1,"quality_controlled":"1","doi":"10.1007/s00440-022-01156-7","publication_identifier":{"issn":["0178-8051"],"eissn":["1432-2064"]},"article_type":"original","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)"},"scopus_import":"1","article_processing_charge":"Yes (via OA deal)","publication":"Probability Theory and Related Fields","department":[{"_id":"LaEr"}],"publisher":"Springer Nature","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"Quenched universality for deformed Wigner matrices","arxiv":1,"day":"01","file":[{"checksum":"b9247827dae5544d1d19c37abe547abc","file_id":"14054","date_updated":"2023-08-14T12:47:32Z","access_level":"open_access","date_created":"2023-08-14T12:47:32Z","file_name":"2023_ProbabilityTheory_Cipolloni.pdf","success":1,"creator":"dernst","file_size":782278,"content_type":"application/pdf","relation":"main_file"}],"author":[{"orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio","first_name":"Giorgio","last_name":"Cipolloni"},{"full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","first_name":"László","last_name":"Erdös"},{"full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","last_name":"Schröder","first_name":"Dominik J"}],"citation":{"ista":"Cipolloni G, Erdös L, Schröder DJ. 2023. Quenched universality for deformed Wigner matrices. Probability Theory and Related Fields. 185, 1183–1218.","mla":"Cipolloni, Giorgio, et al. “Quenched Universality for Deformed Wigner Matrices.” <i>Probability Theory and Related Fields</i>, vol. 185, Springer Nature, 2023, pp. 1183–1218, doi:<a href=\"https://doi.org/10.1007/s00440-022-01156-7\">10.1007/s00440-022-01156-7</a>.","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2023). Quenched universality for deformed Wigner matrices. <i>Probability Theory and Related Fields</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00440-022-01156-7\">https://doi.org/10.1007/s00440-022-01156-7</a>","ama":"Cipolloni G, Erdös L, Schröder DJ. Quenched universality for deformed Wigner matrices. <i>Probability Theory and Related Fields</i>. 2023;185:1183–1218. doi:<a href=\"https://doi.org/10.1007/s00440-022-01156-7\">10.1007/s00440-022-01156-7</a>","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Probability Theory and Related Fields 185 (2023) 1183–1218.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Quenched universality for deformed Wigner matrices,” <i>Probability Theory and Related Fields</i>, vol. 185. Springer Nature, pp. 1183–1218, 2023.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Quenched Universality for Deformed Wigner Matrices.” <i>Probability Theory and Related Fields</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00440-022-01156-7\">https://doi.org/10.1007/s00440-022-01156-7</a>."},"intvolume":"       185","status":"public","external_id":{"isi":["000830344500001"],"arxiv":["2106.10200"]},"ddc":["510"],"date_published":"2023-04-01T00:00:00Z","has_accepted_license":"1","oa":1,"publication_status":"published","_id":"11741","year":"2023","acknowledgement":"The authors are indebted to Sourav Chatterjee for forwarding the very inspiring question that Stephen Shenker originally addressed to him which initiated the current paper. They are also grateful that the authors of [23] kindly shared their preliminary numerical results in June 2021.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria).","date_created":"2022-08-07T22:02:00Z","file_date_updated":"2023-08-14T12:47:32Z","volume":185,"type":"journal_article","month":"04","oa_version":"Published Version","abstract":[{"lang":"eng","text":"Following E. Wigner’s original vision, we prove that sampling the eigenvalue gaps within the bulk spectrum of a fixed (deformed) Wigner matrix H yields the celebrated Wigner-Dyson-Mehta universal statistics with high probability. Similarly, we prove universality for a monoparametric family of deformed Wigner matrices H+xA with a deterministic Hermitian matrix A and a fixed Wigner matrix H, just using the randomness of a single scalar real random variable x. Both results constitute quenched versions of bulk universality that has so far only been proven in annealed sense with respect to the probability space of the matrix ensemble."}],"date_updated":"2023-08-14T12:48:09Z","page":"1183–1218"},{"volume":11,"file_date_updated":"2023-09-20T11:09:35Z","date_created":"2023-09-17T22:01:09Z","oa_version":"Published Version","type":"journal_article","month":"08","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."}],"date_updated":"2023-12-13T12:24:23Z","_id":"14343","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","date_published":"2023-08-23T00:00:00Z","ddc":["510"],"publication_status":"published","oa":1,"has_accepted_license":"1","intvolume":"        11","citation":{"short":"G. Cipolloni, L. Erdös, S.J. Henheik, O. Kolupaiev, Forum of Mathematics, Sigma 11 (2023).","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.","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>.","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>.","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.","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>","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>"},"status":"public","external_id":{"isi":["001051980200001"],"arxiv":["2301.05181"]},"article_number":"e74","arxiv":1,"title":"Gaussian fluctuations in the equipartition principle for Wigner matrices","author":[{"first_name":"Giorgio","last_name":"Cipolloni","full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","last_name":"Erdös"},{"first_name":"Sven Joscha","last_name":"Henheik","full_name":"Henheik, Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","orcid":"0000-0003-1106-327X"},{"first_name":"Oleksii","last_name":"Kolupaiev","full_name":"Kolupaiev, Oleksii","id":"149b70d4-896a-11ed-bdf8-8c63fd44ca61"}],"file":[{"date_updated":"2023-09-20T11:09:35Z","file_id":"14352","checksum":"eb747420e6a88a7796fa934151957676","date_created":"2023-09-20T11:09:35Z","access_level":"open_access","success":1,"file_name":"2023_ForumMathematics_Cipolloni.pdf","content_type":"application/pdf","relation":"main_file","file_size":852652,"creator":"dernst"}],"day":"23","publication":"Forum of Mathematics, Sigma","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","scopus_import":"1","ec_funded":1,"article_processing_charge":"Yes","publisher":"Cambridge University Press","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"LaEr"},{"_id":"GradSch"}],"doi":"10.1017/fms.2023.70","quality_controlled":"1","publication_identifier":{"eissn":["2050-5094"]},"isi":1,"language":[{"iso":"eng"}],"project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","grant_number":"101020331"}]},{"oa":1,"publication_status":"epub_ahead","date_published":"2023-09-28T00:00:00Z","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2210.12060","open_access":"1"}],"status":"public","external_id":{"arxiv":["2210.12060"]},"citation":{"ama":"Cipolloni G, Erdös L, Schröder DJ. Mesoscopic central limit theorem for non-Hermitian random matrices. <i>Probability Theory and Related Fields</i>. 2023. doi:<a href=\"https://doi.org/10.1007/s00440-023-01229-1\">10.1007/s00440-023-01229-1</a>","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2023). Mesoscopic central limit theorem for non-Hermitian random matrices. <i>Probability Theory and Related Fields</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00440-023-01229-1\">https://doi.org/10.1007/s00440-023-01229-1</a>","mla":"Cipolloni, Giorgio, et al. “Mesoscopic Central Limit Theorem for Non-Hermitian Random Matrices.” <i>Probability Theory and Related Fields</i>, Springer Nature, 2023, doi:<a href=\"https://doi.org/10.1007/s00440-023-01229-1\">10.1007/s00440-023-01229-1</a>.","ista":"Cipolloni G, Erdös L, Schröder DJ. 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.” <i>Probability Theory and Related Fields</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00440-023-01229-1\">https://doi.org/10.1007/s00440-023-01229-1</a>.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Mesoscopic central limit theorem for non-Hermitian random matrices,” <i>Probability Theory and Related Fields</i>. Springer Nature, 2023.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Probability Theory and Related Fields (2023)."},"abstract":[{"lang":"eng","text":"We prove that the mesoscopic linear statistics ∑if(na(σi−z0)) of the eigenvalues {σi}i of large n×n non-Hermitian random matrices with complex centred i.i.d. entries are asymptotically Gaussian for any H20-functions f around any point z0 in the bulk of the spectrum on any mesoscopic scale 0<a<1/2. This extends our previous result (Cipolloni et al. in Commun Pure Appl Math, 2019. arXiv:1912.04100), that was valid on the macroscopic scale, a=0\r\n, to cover the entire mesoscopic regime. The main novelty is a local law for the product of resolvents for the Hermitization of X at spectral parameters z1,z2 with an improved error term in the entire mesoscopic regime |z1−z2|≫n−1/2. The proof is dynamical; it relies on a recursive tandem of the characteristic flow method and the Green function comparison idea combined with a separation of the unstable mode of the underlying stability operator."}],"date_updated":"2023-10-09T07:19:01Z","type":"journal_article","oa_version":"Preprint","month":"09","date_created":"2023-10-08T22:01:17Z","acknowledgement":"The authors are grateful to Joscha Henheik for his help with the formulas in Appendix B.","year":"2023","_id":"14408","publication_identifier":{"issn":["0178-8051"],"eissn":["1432-2064"]},"doi":"10.1007/s00440-023-01229-1","quality_controlled":"1","language":[{"iso":"eng"}],"author":[{"first_name":"Giorgio","last_name":"Cipolloni","orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio"},{"last_name":"Erdös","first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László"},{"last_name":"Schröder","first_name":"Dominik J","full_name":"Schröder, Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856"}],"day":"28","title":"Mesoscopic central limit theorem for non-Hermitian random matrices","arxiv":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Springer Nature","department":[{"_id":"LaEr"}],"publication":"Probability Theory and Related Fields","scopus_import":"1","article_processing_charge":"No","article_type":"original"},{"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2112.11382","open_access":"1"}],"date_published":"2023-11-01T00:00:00Z","oa":1,"publication_status":"published","citation":{"apa":"Erdös, L., &#38; Ji, H. C. (2023). Functional CLT for non-Hermitian random matrices. <i>Annales de l’institut Henri Poincare (B) Probability and Statistics</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/22-AIHP1304\">https://doi.org/10.1214/22-AIHP1304</a>","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.","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>.","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>","short":"L. Erdös, H.C. Ji, Annales de l’institut Henri Poincare (B) Probability and Statistics 59 (2023) 2083–2105.","chicago":"Erdös, László, and Hong Chang Ji. “Functional CLT for Non-Hermitian Random Matrices.” <i>Annales de l’institut Henri Poincare (B) Probability and Statistics</i>. Institute of Mathematical Statistics, 2023. <a href=\"https://doi.org/10.1214/22-AIHP1304\">https://doi.org/10.1214/22-AIHP1304</a>.","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."},"intvolume":"        59","status":"public","external_id":{"arxiv":["2112.11382"]},"date_created":"2023-12-10T23:01:00Z","volume":59,"oa_version":"Preprint","type":"journal_article","month":"11","date_updated":"2023-12-11T12:36:56Z","abstract":[{"lang":"eng","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":"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."}],"page":"2083-2105","_id":"14667","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.","quality_controlled":"1","doi":"10.1214/22-AIHP1304","publication_identifier":{"issn":["0246-0203"]},"issue":"4","language":[{"iso":"eng"}],"project":[{"grant_number":"101020331","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"arxiv":1,"title":"Functional CLT for non-Hermitian random matrices","day":"01","author":[{"full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","last_name":"Erdös","first_name":"László"},{"full_name":"Ji, Hong Chang","id":"dd216c0a-c1f9-11eb-beaf-e9ea9d2de76d","first_name":"Hong Chang","last_name":"Ji"}],"article_type":"original","scopus_import":"1","ec_funded":1,"article_processing_charge":"No","publication":"Annales de l'institut Henri Poincare (B) Probability and Statistics","department":[{"_id":"LaEr"}],"publisher":"Institute of Mathematical Statistics","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"publication_identifier":{"issn":["0091-1798"]},"doi":"10.1214/23-aop1643","quality_controlled":"1","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331"}],"keyword":["Statistics","Probability and Uncertainty","Statistics and Probability"],"language":[{"iso":"eng"}],"issue":"6","author":[{"first_name":"Giorgio","last_name":"Cipolloni","full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","first_name":"László","last_name":"Erdös"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J","first_name":"Dominik J","last_name":"Schröder"},{"full_name":"Xu, Yuanyuan","first_name":"Yuanyuan","last_name":"Xu"}],"day":"01","title":"On the rightmost eigenvalue of non-Hermitian random matrices","arxiv":1,"publisher":"Institute of Mathematical Statistics","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"LaEr"}],"publication":"The Annals of Probability","ec_funded":1,"article_processing_charge":"No","article_type":"original","publication_status":"published","oa":1,"date_published":"2023-11-01T00:00:00Z","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2206.04448"}],"external_id":{"arxiv":["2206.04448"]},"status":"public","intvolume":"        51","citation":{"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>.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Y. Xu, The Annals of Probability 51 (2023) 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>","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.","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>.","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>"},"page":"2192-2242","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."}],"date_updated":"2024-01-23T10:56:30Z","oa_version":"Preprint","type":"journal_article","month":"11","volume":51,"date_created":"2024-01-22T08:08:41Z","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.","year":"2023","_id":"14849"},{"publication_identifier":{"issn":["0022-4715"],"eissn":["1572-9613"]},"quality_controlled":"1","doi":"10.1007/s10955-023-03132-4","project":[{"grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"language":[{"iso":"eng"}],"issue":"7","isi":1,"file":[{"creator":"dernst","file_size":612755,"relation":"main_file","content_type":"application/pdf","file_name":"2023_JourStatPhysics_Sugimoto.pdf","success":1,"access_level":"open_access","date_created":"2023-07-31T07:49:31Z","checksum":"c2ef6b2aecfee1ad6d03fab620507c2c","file_id":"13325","date_updated":"2023-07-31T07:49:31Z"}],"day":"21","author":[{"last_name":"Sugimoto","first_name":"Shoki","full_name":"Sugimoto, Shoki"},{"last_name":"Henheik","first_name":"Sven Joscha","full_name":"Henheik, Sven Joscha","orcid":"0000-0003-1106-327X","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb"},{"first_name":"Volodymyr","last_name":"Riabov","id":"1949f904-edfb-11eb-afb5-e2dfddabb93b","full_name":"Riabov, Volodymyr"},{"first_name":"László","last_name":"Erdös","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"}],"arxiv":1,"title":"Eigenstate thermalisation hypothesis for translation invariant spin systems","article_number":"128","department":[{"_id":"LaEr"}],"publisher":"Springer Nature","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","ec_funded":1,"scopus_import":"1","article_processing_charge":"Yes (in subscription journal)","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","publication":"Journal of Statistical Physics","has_accepted_license":"1","publication_status":"published","oa":1,"date_published":"2023-07-21T00:00:00Z","ddc":["510","530"],"external_id":{"isi":["001035677200002"],"arxiv":["2304.04213"]},"status":"public","citation":{"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.","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>.","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>","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>","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.","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>."},"intvolume":"       190","abstract":[{"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.","lang":"eng"}],"date_updated":"2023-12-13T11:38:44Z","oa_version":"Published Version","type":"journal_article","month":"07","date_created":"2023-07-30T22:01:02Z","file_date_updated":"2023-07-31T07:49:31Z","volume":190,"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.","_id":"13317"},{"external_id":{"isi":["000724652500001"],"arxiv":["1912.04100"]},"status":"public","intvolume":"        76","citation":{"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.","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>","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>","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.","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>."},"oa":1,"publication_status":"published","has_accepted_license":"1","ddc":["510"],"date_published":"2023-05-01T00:00:00Z","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.","year":"2023","_id":"10405","page":"946-1034","oa_version":"Published Version","type":"journal_article","month":"05","date_updated":"2023-10-04T09:22:55Z","abstract":[{"lang":"eng","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]. "}],"volume":76,"date_created":"2021-12-05T23:01:41Z","file_date_updated":"2023-10-04T09:21:48Z","project":[{"grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems"},{"grant_number":"665385","name":"International IST Doctoral Program","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"isi":1,"issue":"5","language":[{"iso":"eng"}],"publication_identifier":{"issn":["0010-3640"],"eissn":["1097-0312"]},"doi":"10.1002/cpa.22028","quality_controlled":"1","publisher":"Wiley","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"LaEr"}],"publication":"Communications on Pure and Applied Mathematics","article_type":"original","tmp":{"name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","short":"CC BY-NC-ND (4.0)","image":"/images/cc_by_nc_nd.png","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode"},"ec_funded":1,"article_processing_charge":"Yes (via OA deal)","scopus_import":"1","author":[{"first_name":"Giorgio","last_name":"Cipolloni","full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Erdös","first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László"},{"first_name":"Dominik J","last_name":"Schröder","id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J"}],"file":[{"creator":"dernst","content_type":"application/pdf","relation":"main_file","file_size":803440,"success":1,"file_name":"2023_CommPureMathematics_Cipolloni.pdf","access_level":"open_access","date_created":"2023-10-04T09:21:48Z","checksum":"8346bc2642afb4ccb7f38979f41df5d9","date_updated":"2023-10-04T09:21:48Z","file_id":"14388"}],"day":"01","title":"Central limit theorem for linear eigenvalue statistics of non-Hermitian random matrices","arxiv":1},{"publication_identifier":{"eissn":["1083-589X"]},"quality_controlled":"1","doi":"10.1214/23-ECP516","project":[{"call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"},{"name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331"}],"language":[{"iso":"eng"}],"isi":1,"file":[{"date_created":"2023-02-27T09:43:27Z","access_level":"open_access","date_updated":"2023-02-27T09:43:27Z","file_id":"12692","checksum":"a1c6f0a3e33688fd71309c86a9aad86e","content_type":"application/pdf","relation":"main_file","file_size":479105,"creator":"dernst","success":1,"file_name":"2023_ElectCommProbability_Dubach.pdf"}],"day":"08","author":[{"full_name":"Dubach, Guillaume","orcid":"0000-0001-6892-8137","id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E","first_name":"Guillaume","last_name":"Dubach"},{"last_name":"Erdös","first_name":"László","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603"}],"title":"Dynamics of a rank-one perturbation of a Hermitian matrix","arxiv":1,"department":[{"_id":"LaEr"}],"publisher":"Institute of Mathematical Statistics","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","ec_funded":1,"article_processing_charge":"No","scopus_import":"1","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","publication":"Electronic Communications in Probability","has_accepted_license":"1","oa":1,"publication_status":"published","date_published":"2023-02-08T00:00:00Z","ddc":["510"],"status":"public","external_id":{"isi":["000950650200005"],"arxiv":["2108.13694"]},"citation":{"chicago":"Dubach, Guillaume, and László Erdös. “Dynamics of a Rank-One Perturbation of a Hermitian Matrix.” <i>Electronic Communications in Probability</i>. Institute of Mathematical Statistics, 2023. <a href=\"https://doi.org/10.1214/23-ECP516\">https://doi.org/10.1214/23-ECP516</a>.","ieee":"G. Dubach and L. Erdös, “Dynamics of a rank-one perturbation of a Hermitian matrix,” <i>Electronic Communications in Probability</i>, vol. 28. Institute of Mathematical Statistics, pp. 1–13, 2023.","short":"G. Dubach, L. Erdös, Electronic Communications in Probability 28 (2023) 1–13.","ama":"Dubach G, Erdös L. Dynamics of a rank-one perturbation of a Hermitian matrix. <i>Electronic Communications in Probability</i>. 2023;28:1-13. doi:<a href=\"https://doi.org/10.1214/23-ECP516\">10.1214/23-ECP516</a>","apa":"Dubach, G., &#38; Erdös, L. (2023). Dynamics of a rank-one perturbation of a Hermitian matrix. <i>Electronic Communications in Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/23-ECP516\">https://doi.org/10.1214/23-ECP516</a>","mla":"Dubach, Guillaume, and László Erdös. “Dynamics of a Rank-One Perturbation of a Hermitian Matrix.” <i>Electronic Communications in Probability</i>, vol. 28, Institute of Mathematical Statistics, 2023, pp. 1–13, doi:<a href=\"https://doi.org/10.1214/23-ECP516\">10.1214/23-ECP516</a>.","ista":"Dubach G, Erdös L. 2023. Dynamics of a rank-one perturbation of a Hermitian matrix. Electronic Communications in Probability. 28, 1–13."},"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."}],"date_updated":"2023-10-17T12:48:10Z","oa_version":"Published Version","month":"02","type":"journal_article","page":"1-13","date_created":"2023-02-26T23:01:01Z","file_date_updated":"2023-02-27T09:43:27Z","volume":28,"year":"2023","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.","_id":"12683"},{"publication_status":"published","oa":1,"date_published":"2023-05-01T00:00:00Z","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2112.12093"}],"status":"public","external_id":{"isi":["000947270100008"],"arxiv":["2112.12093 "]},"intvolume":"        29","citation":{"short":"L. Erdös, Y. Xu, Bernoulli 29 (2023) 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.","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>.","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>.","ista":"Erdös L, Xu Y. 2023. Small deviation estimates for the largest eigenvalue of Wigner matrices. Bernoulli. 29(2), 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>","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>"},"page":"1063-1079","date_updated":"2023-10-04T10:21:07Z","abstract":[{"lang":"eng","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."}],"oa_version":"Preprint","month":"05","type":"journal_article","volume":29,"date_created":"2023-03-05T23:01:05Z","year":"2023","_id":"12707","publication_identifier":{"issn":["1350-7265"]},"doi":"10.3150/22-BEJ1490","quality_controlled":"1","project":[{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"}],"isi":1,"language":[{"iso":"eng"}],"issue":"2","author":[{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","first_name":"László","last_name":"Erdös"},{"last_name":"Xu","first_name":"Yuanyuan","orcid":"0000-0003-1559-1205","id":"7902bdb1-a2a4-11eb-a164-c9216f71aea3","full_name":"Xu, Yuanyuan"}],"day":"01","title":"Small deviation estimates for the largest eigenvalue of Wigner matrices","arxiv":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Bernoulli Society for Mathematical Statistics and Probability","department":[{"_id":"LaEr"}],"publication":"Bernoulli","scopus_import":"1","article_processing_charge":"No","ec_funded":1,"article_type":"original"},{"page":"447-489","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"}],"date_updated":"2023-10-17T12:48:52Z","type":"journal_article","month":"02","oa_version":"Preprint","volume":33,"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.","year":"2023","_id":"12761","publication_status":"published","oa":1,"date_published":"2023-02-01T00:00:00Z","main_file_link":[{"url":"https://arxiv.org/abs/2012.13218","open_access":"1"}],"external_id":{"arxiv":["2012.13218"],"isi":["000946432400015"]},"status":"public","intvolume":"        33","citation":{"ista":"Cipolloni G, Erdös L, Schröder DJ. 2023. Functional central limit theorems for Wigner matrices. Annals of Applied Probability. 33(1), 447–489.","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>.","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>","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>","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.","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>."},"author":[{"first_name":"Giorgio","last_name":"Cipolloni","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio"},{"first_name":"László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","full_name":"Erdös, László"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J","last_name":"Schröder","first_name":"Dominik J"}],"day":"01","arxiv":1,"title":"Functional central limit theorems for Wigner matrices","publisher":"Institute of Mathematical Statistics","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"LaEr"}],"publication":"Annals of Applied Probability","article_processing_charge":"No","ec_funded":1,"scopus_import":"1","article_type":"original","publication_identifier":{"issn":["1050-5164"]},"doi":"10.1214/22-AAP1820","quality_controlled":"1","project":[{"grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"isi":1,"language":[{"iso":"eng"}],"issue":"1"},{"volume":401,"date_created":"2023-04-02T22:01:11Z","file_date_updated":"2023-10-04T12:09:18Z","page":"1665-1700","oa_version":"Published Version","type":"journal_article","month":"07","abstract":[{"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.","lang":"eng"}],"date_updated":"2023-10-04T12:10:31Z","_id":"12792","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","ddc":["510"],"date_published":"2023-07-01T00:00:00Z","publication_status":"published","oa":1,"has_accepted_license":"1","intvolume":"       401","citation":{"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>","ista":"Cipolloni G, Erdös L, Schröder DJ. 2023. On the spectral form factor for random matrices. Communications in Mathematical Physics. 401, 1665–1700.","mla":"Cipolloni, Giorgio, et al. “On the Spectral Form Factor for Random Matrices.” <i>Communications in Mathematical Physics</i>, vol. 401, Springer Nature, 2023, pp. 1665–700, doi:<a href=\"https://doi.org/10.1007/s00220-023-04692-y\">10.1007/s00220-023-04692-y</a>.","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>","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.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “On the Spectral Form Factor for Random Matrices.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00220-023-04692-y\">https://doi.org/10.1007/s00220-023-04692-y</a>.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Communications in Mathematical Physics 401 (2023) 1665–1700."},"external_id":{"isi":["000957343500001"]},"status":"public","title":"On the spectral form factor for random matrices","author":[{"full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","last_name":"Cipolloni","first_name":"Giorgio"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös","first_name":"László"},{"last_name":"Schröder","first_name":"Dominik J","full_name":"Schröder, Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856"}],"file":[{"file_name":"2023_CommMathPhysics_Cipolloni.pdf","success":1,"creator":"dernst","file_size":859967,"relation":"main_file","content_type":"application/pdf","checksum":"72057940f76654050ca84a221f21786c","file_id":"14397","date_updated":"2023-10-04T12:09:18Z","access_level":"open_access","date_created":"2023-10-04T12:09:18Z"}],"day":"01","publication":"Communications in Mathematical Physics","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","ec_funded":1,"scopus_import":"1","article_processing_charge":"Yes (via OA deal)","publisher":"Springer Nature","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"LaEr"}],"doi":"10.1007/s00220-023-04692-y","quality_controlled":"1","publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"isi":1,"language":[{"iso":"eng"}],"project":[{"grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta"}]},{"title":"Thermalisation for Wigner matrices","arxiv":1,"article_number":"109394","author":[{"last_name":"Cipolloni","first_name":"Giorgio","full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"László","last_name":"Erdös","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603"},{"full_name":"Schröder, Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856","first_name":"Dominik J","last_name":"Schröder"}],"file":[{"file_size":652573,"relation":"main_file","content_type":"application/pdf","creator":"dernst","file_name":"2022_JourFunctionalAnalysis_Cipolloni.pdf","success":1,"date_created":"2022-07-29T07:22:08Z","access_level":"open_access","file_id":"11690","date_updated":"2022-07-29T07:22:08Z","checksum":"b75fdad606ab507dc61109e0907d86c0"}],"day":"15","publication":"Journal of Functional Analysis","scopus_import":"1","article_processing_charge":"Yes (via OA deal)","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","publisher":"Elsevier","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","department":[{"_id":"LaEr"}],"doi":"10.1016/j.jfa.2022.109394","quality_controlled":"1","publication_identifier":{"eissn":["1096-0783"],"issn":["0022-1236"]},"isi":1,"language":[{"iso":"eng"}],"issue":"8","volume":282,"date_created":"2022-02-06T23:01:30Z","file_date_updated":"2022-07-29T07:22:08Z","date_updated":"2023-08-02T14:12:35Z","abstract":[{"text":"We compute the deterministic approximation of products of Sobolev functions of large Wigner matrices W and provide an optimal error bound on their fluctuation with very high probability. This generalizes Voiculescu's seminal theorem from polynomials to general Sobolev functions, as well as from tracial quantities to individual matrix elements. Applying the result to eitW for large t, we obtain a precise decay rate for the overlaps of several deterministic matrices with temporally well separated Heisenberg time evolutions; thus we demonstrate the thermalisation effect of the unitary group generated by Wigner matrices.","lang":"eng"}],"type":"journal_article","month":"04","oa_version":"Published Version","_id":"10732","acknowledgement":"We compute the deterministic approximation of products of Sobolev functions of large Wigner matrices W and provide an optimal error bound on their fluctuation with very high probability. This generalizes Voiculescu's seminal theorem from polynomials to general Sobolev functions, as well as from tracial quantities to individual matrix elements. Applying the result to  for large t, we obtain a precise decay rate for the overlaps of several deterministic matrices with temporally well separated Heisenberg time evolutions; thus we demonstrate the thermalisation effect of the unitary group generated by Wigner matrices.","year":"2022","ddc":["500"],"date_published":"2022-04-15T00:00:00Z","oa":1,"publication_status":"published","has_accepted_license":"1","intvolume":"       282","citation":{"ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Thermalisation for Wigner matrices,” <i>Journal of Functional Analysis</i>, vol. 282, no. 8. Elsevier, 2022.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Thermalisation for Wigner Matrices.” <i>Journal of Functional Analysis</i>. Elsevier, 2022. <a href=\"https://doi.org/10.1016/j.jfa.2022.109394\">https://doi.org/10.1016/j.jfa.2022.109394</a>.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Journal of Functional Analysis 282 (2022).","ama":"Cipolloni G, Erdös L, Schröder DJ. Thermalisation for Wigner matrices. <i>Journal of Functional Analysis</i>. 2022;282(8). doi:<a href=\"https://doi.org/10.1016/j.jfa.2022.109394\">10.1016/j.jfa.2022.109394</a>","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Thermalisation for Wigner matrices. Journal of Functional Analysis. 282(8), 109394.","mla":"Cipolloni, Giorgio, et al. “Thermalisation for Wigner Matrices.” <i>Journal of Functional Analysis</i>, vol. 282, no. 8, 109394, Elsevier, 2022, doi:<a href=\"https://doi.org/10.1016/j.jfa.2022.109394\">10.1016/j.jfa.2022.109394</a>.","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2022). Thermalisation for Wigner matrices. <i>Journal of Functional Analysis</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jfa.2022.109394\">https://doi.org/10.1016/j.jfa.2022.109394</a>"},"status":"public","external_id":{"arxiv":["2102.09975"],"isi":["000781239100004"]}},{"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","_id":"11418","page":"984-1012","oa_version":"Preprint","month":"05","type":"journal_article","date_updated":"2023-08-03T07:16:53Z","abstract":[{"lang":"eng","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)."}],"volume":50,"date_created":"2022-05-29T22:01:53Z","status":"public","external_id":{"isi":["000793963400005"],"arxiv":["2103.06730"]},"intvolume":"        50","citation":{"apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2022). Normal fluctuation in quantum ergodicity for Wigner matrices. <i>Annals of Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/21-AOP1552\">https://doi.org/10.1214/21-AOP1552</a>","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>","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Annals of Probability 50 (2022) 984–1012.","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>.","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."},"publication_status":"published","oa":1,"date_published":"2022-05-01T00:00:00Z","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2103.06730"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publisher":"Institute of Mathematical Statistics","department":[{"_id":"LaEr"}],"publication":"Annals of Probability","article_type":"original","scopus_import":"1","article_processing_charge":"No","author":[{"full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","last_name":"Cipolloni","first_name":"Giorgio"},{"orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","first_name":"László","last_name":"Erdös"},{"orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","full_name":"Schröder, Dominik J","first_name":"Dominik J","last_name":"Schröder"}],"day":"01","arxiv":1,"title":"Normal fluctuation in quantum ergodicity for Wigner matrices","isi":1,"issue":"3","language":[{"iso":"eng"}],"publication_identifier":{"eissn":["2168-894X"],"issn":["0091-1798"]},"doi":"10.1214/21-AOP1552","quality_controlled":"1"},{"month":"10","oa_version":"Published Version","type":"journal_article","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"}],"date_updated":"2023-08-04T09:00:35Z","volume":10,"date_created":"2023-01-12T12:07:30Z","file_date_updated":"2023-01-24T10:02:40Z","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.","year":"2022","_id":"12148","publication_status":"published","oa":1,"has_accepted_license":"1","ddc":["510"],"date_published":"2022-10-27T00:00:00Z","external_id":{"isi":["000873719200001"]},"status":"public","intvolume":"        10","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.","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>.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Forum of Mathematics, Sigma 10 (2022).","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>","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>.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Rank-uniform local law for Wigner matrices. Forum of Mathematics, Sigma. 10, e96.","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>"},"author":[{"full_name":"Cipolloni, Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992","first_name":"Giorgio","last_name":"Cipolloni"},{"full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","first_name":"László","last_name":"Erdös"},{"orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","full_name":"Schröder, Dominik J","last_name":"Schröder","first_name":"Dominik J"}],"day":"27","file":[{"access_level":"open_access","date_created":"2023-01-24T10:02:40Z","checksum":"94a049aeb1eea5497aa097712a73c400","file_id":"12356","date_updated":"2023-01-24T10:02:40Z","creator":"dernst","file_size":817089,"relation":"main_file","content_type":"application/pdf","file_name":"2022_ForumMath_Cipolloni.pdf","success":1}],"article_number":"e96","title":"Rank-uniform local law for Wigner matrices","publisher":"Cambridge University Press","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","department":[{"_id":"LaEr"}],"publication":"Forum of Mathematics, Sigma","article_type":"original","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_processing_charge":"No","ec_funded":1,"scopus_import":"1","publication_identifier":{"issn":["2050-5094"]},"doi":"10.1017/fms.2022.86","quality_controlled":"1","project":[{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"}],"keyword":["Computational Mathematics","Discrete Mathematics and Combinatorics","Geometry and Topology","Mathematical Physics","Statistics and Probability","Algebra and Number Theory","Theoretical Computer Science","Analysis"],"isi":1,"language":[{"iso":"eng"}]},{"publication_identifier":{"issn":["0895-4798"],"eissn":["1095-7162"]},"doi":"10.1137/21m1424408","quality_controlled":"1","keyword":["Analysis"],"language":[{"iso":"eng"}],"issue":"3","author":[{"first_name":"Giorgio","last_name":"Cipolloni","full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös","first_name":"László"},{"orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","full_name":"Schröder, Dominik J","last_name":"Schröder","first_name":"Dominik J"}],"day":"01","arxiv":1,"title":"On the condition number of the shifted real Ginibre ensemble","publisher":"Society for Industrial and Applied Mathematics","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"LaEr"}],"publication":"SIAM Journal on Matrix Analysis and Applications","scopus_import":"1","article_processing_charge":"No","article_type":"original","publication_status":"published","oa":1,"date_published":"2022-07-01T00:00:00Z","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2105.13719"}],"status":"public","external_id":{"arxiv":["2105.13719"]},"intvolume":"        43","citation":{"ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “On the condition number of the shifted real Ginibre ensemble,” <i>SIAM Journal on Matrix Analysis and Applications</i>, vol. 43, no. 3. Society for Industrial and Applied Mathematics, pp. 1469–1487, 2022.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “On the Condition Number of the Shifted Real Ginibre Ensemble.” <i>SIAM Journal on Matrix Analysis and Applications</i>. Society for Industrial and Applied Mathematics, 2022. <a href=\"https://doi.org/10.1137/21m1424408\">https://doi.org/10.1137/21m1424408</a>.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, SIAM Journal on Matrix Analysis and Applications 43 (2022) 1469–1487.","ama":"Cipolloni G, Erdös L, Schröder DJ. On the condition number of the shifted real Ginibre ensemble. <i>SIAM Journal on Matrix Analysis and Applications</i>. 2022;43(3):1469-1487. doi:<a href=\"https://doi.org/10.1137/21m1424408\">10.1137/21m1424408</a>","mla":"Cipolloni, Giorgio, et al. “On the Condition Number of the Shifted Real Ginibre Ensemble.” <i>SIAM Journal on Matrix Analysis and Applications</i>, vol. 43, no. 3, Society for Industrial and Applied Mathematics, 2022, pp. 1469–87, doi:<a href=\"https://doi.org/10.1137/21m1424408\">10.1137/21m1424408</a>.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. On the condition number of the shifted real Ginibre ensemble. SIAM Journal on Matrix Analysis and Applications. 43(3), 1469–1487.","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2022). On the condition number of the shifted real Ginibre ensemble. <i>SIAM Journal on Matrix Analysis and Applications</i>. Society for Industrial and Applied Mathematics. <a href=\"https://doi.org/10.1137/21m1424408\">https://doi.org/10.1137/21m1424408</a>"},"page":"1469-1487","abstract":[{"lang":"eng","text":"We derive an accurate lower tail estimate on the lowest singular value σ1(X−z) of a real Gaussian (Ginibre) random matrix X shifted by a complex parameter z. Such shift effectively changes the upper tail behavior of the condition number κ(X−z) from the slower (κ(X−z)≥t)≲1/t decay typical for real Ginibre matrices to the faster 1/t2 decay seen for complex Ginibre matrices as long as z is away from the real axis. This sharpens and resolves a recent conjecture in [J. Banks et al., https://arxiv.org/abs/2005.08930, 2020] on the regularizing effect of the real Ginibre ensemble with a genuinely complex shift. As a consequence we obtain an improved upper bound on the eigenvalue condition numbers (known also as the eigenvector overlaps) for real Ginibre matrices. The main technical tool is a rigorous supersymmetric analysis from our earlier work [Probab. Math. Phys., 1 (2020), pp. 101--146]."}],"date_updated":"2023-01-27T06:56:06Z","month":"07","oa_version":"Preprint","type":"journal_article","volume":43,"date_created":"2023-01-12T12:12:38Z","year":"2022","_id":"12179"},{"title":"Density of small singular values of the shifted real Ginibre ensemble","author":[{"orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio","first_name":"Giorgio","last_name":"Cipolloni"},{"last_name":"Erdös","first_name":"László","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603"},{"last_name":"Schröder","first_name":"Dominik J","full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87"}],"day":"01","file":[{"creator":"dernst","content_type":"application/pdf","relation":"main_file","file_size":1333638,"success":1,"file_name":"2022_AnnalesHenriP_Cipolloni.pdf","access_level":"open_access","date_created":"2023-01-27T11:06:47Z","checksum":"5582f059feeb2f63e2eb68197a34d7dc","date_updated":"2023-01-27T11:06:47Z","file_id":"12424"}],"publication":"Annales Henri Poincaré","article_processing_charge":"No","scopus_import":"1","article_type":"original","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)"},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publisher":"Springer Nature","department":[{"_id":"LaEr"}],"doi":"10.1007/s00023-022-01188-8","quality_controlled":"1","publication_identifier":{"eissn":["1424-0661"],"issn":["1424-0637"]},"isi":1,"keyword":["Mathematical Physics","Nuclear and High Energy Physics","Statistical and Nonlinear Physics"],"language":[{"iso":"eng"}],"issue":"11","volume":23,"date_created":"2023-01-16T09:50:26Z","file_date_updated":"2023-01-27T11:06:47Z","page":"3981-4002","date_updated":"2023-08-04T09:33:52Z","abstract":[{"lang":"eng","text":"We derive a precise asymptotic formula for the density of the small singular values of the real Ginibre matrix ensemble shifted by a complex parameter z as the dimension tends to infinity. For z away from the real axis the formula coincides with that for the complex Ginibre ensemble we derived earlier in Cipolloni et al. (Prob Math Phys 1:101–146, 2020). On the level of the one-point function of the low lying singular values we thus confirm the transition from real to complex Ginibre ensembles as the shift parameter z becomes genuinely complex; the analogous phenomenon has been well known for eigenvalues. We use the superbosonization formula (Littelmann et al. in Comm Math Phys 283:343–395, 2008) in a regime where the main contribution comes from a three dimensional saddle manifold."}],"type":"journal_article","oa_version":"Published Version","month":"11","_id":"12232","acknowledgement":"Open access funding provided by Swiss Federal Institute of Technology Zurich. Supported by Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zürich Foundation.","year":"2022","date_published":"2022-11-01T00:00:00Z","ddc":["510"],"oa":1,"publication_status":"published","has_accepted_license":"1","intvolume":"        23","citation":{"ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Density of small singular values of the shifted real Ginibre ensemble. Annales Henri Poincaré. 23(11), 3981–4002.","mla":"Cipolloni, Giorgio, et al. “Density of Small Singular Values of the Shifted Real Ginibre Ensemble.” <i>Annales Henri Poincaré</i>, vol. 23, no. 11, Springer Nature, 2022, pp. 3981–4002, doi:<a href=\"https://doi.org/10.1007/s00023-022-01188-8\">10.1007/s00023-022-01188-8</a>.","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2022). Density of small singular values of the shifted real Ginibre ensemble. <i>Annales Henri Poincaré</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00023-022-01188-8\">https://doi.org/10.1007/s00023-022-01188-8</a>","ama":"Cipolloni G, Erdös L, Schröder DJ. Density of small singular values of the shifted real Ginibre ensemble. <i>Annales Henri Poincaré</i>. 2022;23(11):3981-4002. doi:<a href=\"https://doi.org/10.1007/s00023-022-01188-8\">10.1007/s00023-022-01188-8</a>","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Annales Henri Poincaré 23 (2022) 3981–4002.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Density of small singular values of the shifted real Ginibre ensemble,” <i>Annales Henri Poincaré</i>, vol. 23, no. 11. Springer Nature, pp. 3981–4002, 2022.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Density of Small Singular Values of the Shifted Real Ginibre Ensemble.” <i>Annales Henri Poincaré</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s00023-022-01188-8\">https://doi.org/10.1007/s00023-022-01188-8</a>."},"status":"public","external_id":{"isi":["000796323500001"]}},{"isi":1,"keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"language":[{"iso":"eng"}],"issue":"10","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","grant_number":"101020331"}],"doi":"10.1063/5.0104290","quality_controlled":"1","publication_identifier":{"eissn":["1089-7658"],"issn":["0022-2488"]},"publication":"Journal of Mathematical Physics","scopus_import":"1","article_processing_charge":"Yes (via OA deal)","ec_funded":1,"article_type":"original","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)"},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publisher":"AIP Publishing","department":[{"_id":"LaEr"}],"arxiv":1,"title":"Directional extremal statistics for Ginibre eigenvalues","article_number":"103303","author":[{"full_name":"Cipolloni, Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992","last_name":"Cipolloni","first_name":"Giorgio"},{"first_name":"László","last_name":"Erdös","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Dominik J","last_name":"Schröder","id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J"},{"last_name":"Xu","first_name":"Yuanyuan","id":"7902bdb1-a2a4-11eb-a164-c9216f71aea3","full_name":"Xu, Yuanyuan"}],"file":[{"checksum":"2db278ae5b07f345a7e3fec1f92b5c33","file_id":"12436","date_updated":"2023-01-30T08:01:10Z","access_level":"open_access","date_created":"2023-01-30T08:01:10Z","file_name":"2022_JourMathPhysics_Cipolloni2.pdf","success":1,"creator":"dernst","file_size":7356807,"relation":"main_file","content_type":"application/pdf"}],"day":"14","intvolume":"        63","citation":{"ama":"Cipolloni G, Erdös L, Schröder DJ, Xu Y. Directional extremal statistics for Ginibre eigenvalues. <i>Journal of Mathematical Physics</i>. 2022;63(10). doi:<a href=\"https://doi.org/10.1063/5.0104290\">10.1063/5.0104290</a>","apa":"Cipolloni, G., Erdös, L., Schröder, D. J., &#38; Xu, Y. (2022). Directional extremal statistics for Ginibre eigenvalues. <i>Journal of Mathematical Physics</i>. AIP Publishing. <a href=\"https://doi.org/10.1063/5.0104290\">https://doi.org/10.1063/5.0104290</a>","ista":"Cipolloni G, Erdös L, Schröder DJ, Xu Y. 2022. Directional extremal statistics for Ginibre eigenvalues. Journal of Mathematical Physics. 63(10), 103303.","mla":"Cipolloni, Giorgio, et al. “Directional Extremal Statistics for Ginibre Eigenvalues.” <i>Journal of Mathematical Physics</i>, vol. 63, no. 10, 103303, AIP Publishing, 2022, doi:<a href=\"https://doi.org/10.1063/5.0104290\">10.1063/5.0104290</a>.","chicago":"Cipolloni, Giorgio, László Erdös, Dominik J Schröder, and Yuanyuan Xu. “Directional Extremal Statistics for Ginibre Eigenvalues.” <i>Journal of Mathematical Physics</i>. AIP Publishing, 2022. <a href=\"https://doi.org/10.1063/5.0104290\">https://doi.org/10.1063/5.0104290</a>.","ieee":"G. Cipolloni, L. Erdös, D. J. Schröder, and Y. Xu, “Directional extremal statistics for Ginibre eigenvalues,” <i>Journal of Mathematical Physics</i>, vol. 63, no. 10. AIP Publishing, 2022.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Y. Xu, Journal of Mathematical Physics 63 (2022)."},"external_id":{"arxiv":["2206.04443"],"isi":["000869715800001"]},"status":"public","date_published":"2022-10-14T00:00:00Z","ddc":["510","530"],"oa":1,"publication_status":"published","has_accepted_license":"1","_id":"12243","acknowledgement":"The authors are grateful to G. Akemann for bringing Refs. 19 and 24–26 to their attention. Discussions with Guillaume Dubach on a preliminary version of this project are acknowledged.\r\nL.E. and Y.X. were supported by the ERC Advanced Grant “RMTBeyond” under Grant No. 101020331. D.S. was supported by Dr. Max Rössler, the Walter Haefner Foundation, and the ETH Zürich Foundation.","year":"2022","volume":63,"file_date_updated":"2023-01-30T08:01:10Z","date_created":"2023-01-16T09:52:58Z","abstract":[{"lang":"eng","text":"We consider the eigenvalues of a large dimensional real or complex Ginibre matrix in the region of the complex plane where their real parts reach their maximum value. This maximum follows the Gumbel distribution and that these extreme eigenvalues form a Poisson point process as the dimension asymptotically tends to infinity. In the complex case, these facts have already been established by Bender [Probab. Theory Relat. Fields 147, 241 (2010)] and in the real case by Akemann and Phillips [J. Stat. Phys. 155, 421 (2014)] even for the more general elliptic ensemble with a sophisticated saddle point analysis. The purpose of this article is to give a very short direct proof in the Ginibre case with an effective error term. Moreover, our estimates on the correlation kernel in this regime serve as a key input for accurately locating [Formula: see text] for any large matrix X with i.i.d. entries in the companion paper [G. Cipolloni et al., arXiv:2206.04448 (2022)]. "}],"date_updated":"2023-08-04T09:40:02Z","type":"journal_article","month":"10","oa_version":"Published Version"},{"year":"2022","acknowledgement":"L. Erdős was supported by ERC Advanced Grant “RMTBeyond” No. 101020331. D. Schröder was supported by Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zürich Foundation.","_id":"12290","date_updated":"2023-08-04T10:32:23Z","abstract":[{"lang":"eng","text":"We prove local laws, i.e. optimal concentration estimates for arbitrary products of resolvents of a Wigner random matrix with deterministic matrices in between. We find that the size of such products heavily depends on whether some of the deterministic matrices are traceless. Our estimates correctly account for this dependence and they hold optimally down to the smallest possible spectral scale."}],"oa_version":"Published Version","month":"09","type":"journal_article","page":"1-38","date_created":"2023-01-16T10:04:38Z","file_date_updated":"2023-01-30T11:59:21Z","volume":27,"status":"public","external_id":{"isi":["000910863700003"]},"citation":{"chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Optimal Multi-Resolvent Local Laws for Wigner Matrices.” <i>Electronic Journal of Probability</i>. Institute of Mathematical Statistics, 2022. <a href=\"https://doi.org/10.1214/22-ejp838\">https://doi.org/10.1214/22-ejp838</a>.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Optimal multi-resolvent local laws for Wigner matrices,” <i>Electronic Journal of Probability</i>, vol. 27. Institute of Mathematical Statistics, pp. 1–38, 2022.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Electronic Journal of Probability 27 (2022) 1–38.","ama":"Cipolloni G, Erdös L, Schröder DJ. Optimal multi-resolvent local laws for Wigner matrices. <i>Electronic Journal of Probability</i>. 2022;27:1-38. doi:<a href=\"https://doi.org/10.1214/22-ejp838\">10.1214/22-ejp838</a>","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2022). Optimal multi-resolvent local laws for Wigner matrices. <i>Electronic Journal of Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/22-ejp838\">https://doi.org/10.1214/22-ejp838</a>","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Optimal multi-resolvent local laws for Wigner matrices. Electronic Journal of Probability. 27, 1–38.","mla":"Cipolloni, Giorgio, et al. “Optimal Multi-Resolvent Local Laws for Wigner Matrices.” <i>Electronic Journal of Probability</i>, vol. 27, Institute of Mathematical Statistics, 2022, pp. 1–38, doi:<a href=\"https://doi.org/10.1214/22-ejp838\">10.1214/22-ejp838</a>."},"intvolume":"        27","has_accepted_license":"1","oa":1,"publication_status":"published","date_published":"2022-09-12T00:00:00Z","ddc":["510"],"department":[{"_id":"LaEr"}],"publisher":"Institute of Mathematical Statistics","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","scopus_import":"1","ec_funded":1,"article_processing_charge":"No","article_type":"original","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)"},"publication":"Electronic Journal of Probability","day":"12","file":[{"file_id":"12464","date_updated":"2023-01-30T11:59:21Z","checksum":"bb647b48fbdb59361210e425c220cdcb","date_created":"2023-01-30T11:59:21Z","access_level":"open_access","file_name":"2022_ElecJournProbability_Cipolloni.pdf","success":1,"file_size":502149,"relation":"main_file","content_type":"application/pdf","creator":"dernst"}],"author":[{"first_name":"Giorgio","last_name":"Cipolloni","full_name":"Cipolloni, Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992"},{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","first_name":"László"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J","first_name":"Dominik J","last_name":"Schröder"}],"title":"Optimal multi-resolvent local laws for Wigner matrices","project":[{"grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"language":[{"iso":"eng"}],"isi":1,"keyword":["Statistics","Probability and Uncertainty","Statistics and Probability"],"publication_identifier":{"eissn":["1083-6489"]},"quality_controlled":"1","doi":"10.1214/22-ejp838"},{"date_updated":"2024-03-07T15:07:53Z","abstract":[{"text":"We consider large non-Hermitian real or complex random matrices X with independent, identically distributed centred entries. We prove that their local eigenvalue statistics near the spectral edge, the unit circle, coincide with those of the Ginibre ensemble, i.e. when the matrix elements of X are Gaussian. This result is the non-Hermitian counterpart of the universality of the Tracy–Widom distribution at the spectral edges of the Wigner ensemble.","lang":"eng"}],"month":"02","type":"journal_article","oa_version":"Published Version","date_created":"2020-10-04T22:01:37Z","file_date_updated":"2020-10-05T14:53:40Z","year":"2021","_id":"8601","has_accepted_license":"1","publication_status":"published","oa":1,"date_published":"2021-02-01T00:00:00Z","ddc":["510"],"status":"public","external_id":{"arxiv":["1908.00969"],"isi":["000572724600002"]},"citation":{"chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Edge Universality for Non-Hermitian Random Matrices.” <i>Probability Theory and Related Fields</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00440-020-01003-7\">https://doi.org/10.1007/s00440-020-01003-7</a>.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Edge universality for non-Hermitian random matrices,” <i>Probability Theory and Related Fields</i>. Springer Nature, 2021.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Probability Theory and Related Fields (2021).","ama":"Cipolloni G, Erdös L, Schröder DJ. Edge universality for non-Hermitian random matrices. <i>Probability Theory and Related Fields</i>. 2021. doi:<a href=\"https://doi.org/10.1007/s00440-020-01003-7\">10.1007/s00440-020-01003-7</a>","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2021). Edge universality for non-Hermitian random matrices. <i>Probability Theory and Related Fields</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00440-020-01003-7\">https://doi.org/10.1007/s00440-020-01003-7</a>","ista":"Cipolloni G, Erdös L, Schröder DJ. 2021. Edge universality for non-Hermitian random matrices. Probability Theory and Related Fields.","mla":"Cipolloni, Giorgio, et al. “Edge Universality for Non-Hermitian Random Matrices.” <i>Probability Theory and Related Fields</i>, Springer Nature, 2021, doi:<a href=\"https://doi.org/10.1007/s00440-020-01003-7\">10.1007/s00440-020-01003-7</a>."},"day":"01","file":[{"file_id":"8612","date_updated":"2020-10-05T14:53:40Z","checksum":"611ae28d6055e1e298d53a57beb05ef4","date_created":"2020-10-05T14:53:40Z","access_level":"open_access","file_name":"2020_ProbTheory_Cipolloni.pdf","success":1,"file_size":497032,"content_type":"application/pdf","relation":"main_file","creator":"dernst"}],"author":[{"first_name":"Giorgio","last_name":"Cipolloni","full_name":"Cipolloni, Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992"},{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","last_name":"Erdös"},{"full_name":"Schröder, Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856","last_name":"Schröder","first_name":"Dominik J"}],"title":"Edge universality for non-Hermitian random matrices","arxiv":1,"department":[{"_id":"LaEr"}],"publisher":"Springer Nature","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"Yes (via OA deal)","ec_funded":1,"scopus_import":"1","article_type":"original","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)"},"publication":"Probability Theory and Related Fields","publication_identifier":{"issn":["01788051"],"eissn":["14322064"]},"quality_controlled":"1","doi":"10.1007/s00440-020-01003-7","project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"},{"grant_number":"338804","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems"},{"grant_number":"665385","name":"International IST Doctoral Program","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"language":[{"iso":"eng"}],"isi":1}]