{"doi":"10.3150/22-BEJ1490","abstract":[{"text":"We establish precise right-tail small deviation estimates for the largest eigenvalue of real symmetric and complex Hermitian matrices whose entries are independent random variables with uniformly bounded moments. The proof relies on a Green function comparison along a continuous interpolating matrix flow for a long time. Less precise estimates are also obtained in the left tail.","lang":"eng"}],"date_created":"2023-03-05T23:01:05Z","publication":"Bernoulli","ec_funded":1,"title":"Small deviation estimates for the largest eigenvalue of Wigner matrices","publication_status":"published","author":[{"full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","first_name":"László","last_name":"Erdös"},{"last_name":"Xu","orcid":"0000-0003-1559-1205","id":"7902bdb1-a2a4-11eb-a164-c9216f71aea3","full_name":"Xu, Yuanyuan","first_name":"Yuanyuan"}],"citation":{"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>","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>","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.","ista":"Erdös L, Xu Y. 2023. Small deviation estimates for the largest eigenvalue of Wigner matrices. Bernoulli. 29(2), 1063–1079.","mla":"Erdös, László, and Yuanyuan Xu. “Small Deviation Estimates for the Largest Eigenvalue of Wigner Matrices.” <i>Bernoulli</i>, vol. 29, no. 2, Bernoulli Society for Mathematical Statistics and Probability, 2023, pp. 1063–79, doi:<a href=\"https://doi.org/10.3150/22-BEJ1490\">10.3150/22-BEJ1490</a>.","chicago":"Erdös, László, and Yuanyuan Xu. “Small Deviation Estimates for the Largest Eigenvalue of Wigner Matrices.” <i>Bernoulli</i>. Bernoulli Society for Mathematical Statistics and Probability, 2023. <a href=\"https://doi.org/10.3150/22-BEJ1490\">https://doi.org/10.3150/22-BEJ1490</a>."},"article_type":"original","quality_controlled":"1","scopus_import":"1","oa":1,"date_published":"2023-05-01T00:00:00Z","date_updated":"2024-10-09T21:04:45Z","isi":1,"arxiv":1,"oa_version":"Preprint","status":"public","publication_identifier":{"issn":["1350-7265"]},"year":"2023","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","language":[{"iso":"eng"}],"publisher":"Bernoulli Society for Mathematical Statistics and Probability","main_file_link":[{"url":"https://arxiv.org/abs/2112.12093","open_access":"1"}],"_id":"12707","department":[{"_id":"LaEr"}],"type":"journal_article","article_processing_charge":"No","page":"1063-1079","intvolume":"        29","issue":"2","volume":29,"month":"05","corr_author":"1","day":"01","external_id":{"isi":["000947270100008"],"arxiv":["2112.12093 "]}}