{"department":[{"_id":"LaEr"}],"abstract":[{"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.","lang":"eng"}],"publication_status":"published","date_published":"2023-04-01T00:00:00Z","article_processing_charge":"Yes (via OA deal)","month":"04","tmp":{"image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"date_updated":"2023-08-14T12:48:09Z","file":[{"success":1,"file_id":"14054","date_created":"2023-08-14T12:47:32Z","file_size":782278,"date_updated":"2023-08-14T12:47:32Z","content_type":"application/pdf","creator":"dernst","access_level":"open_access","file_name":"2023_ProbabilityTheory_Cipolloni.pdf","checksum":"b9247827dae5544d1d19c37abe547abc","relation":"main_file"}],"type":"journal_article","license":"https://creativecommons.org/licenses/by/4.0/","day":"01","title":"Quenched universality for deformed Wigner matrices","quality_controlled":"1","status":"public","publisher":"Springer Nature","scopus_import":"1","oa":1,"oa_version":"Published Version","date_created":"2022-08-07T22:02:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","language":[{"iso":"eng"}],"_id":"11741","citation":{"short":"G. Cipolloni, L. Erdös, D.J. Schröder, Probability Theory and Related Fields 185 (2023) 1183–1218.","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>","ista":"Cipolloni G, Erdös L, Schröder DJ. 2023. Quenched universality for deformed Wigner matrices. Probability Theory and Related Fields. 185, 1183–1218.","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2023). Quenched universality for deformed Wigner matrices. <i>Probability Theory and Related Fields</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00440-022-01156-7\">https://doi.org/10.1007/s00440-022-01156-7</a>","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>.","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.","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>."},"article_type":"original","external_id":{"isi":["000830344500001"],"arxiv":["2106.10200"]},"publication_identifier":{"eissn":["1432-2064"],"issn":["0178-8051"]},"doi":"10.1007/s00440-022-01156-7","page":"1183–1218","publication":"Probability Theory and Related Fields","author":[{"full_name":"Cipolloni, Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","last_name":"Cipolloni","first_name":"Giorgio","orcid":"0000-0002-4901-7992"},{"orcid":"0000-0001-5366-9603","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","last_name":"Erdös"},{"orcid":"0000-0002-2904-1856","first_name":"Dominik J","last_name":"Schröder","full_name":"Schröder, Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87"}],"has_accepted_license":"1","ddc":["510"],"isi":1,"file_date_updated":"2023-08-14T12:47:32Z","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).","year":"2023","intvolume":"       185","volume":185}