{"language":[{"iso":"eng"}],"date_created":"2023-03-05T23:01:05Z","page":"1063-1079","department":[{"_id":"LaEr"}],"oa":1,"doi":"10.3150/22-BEJ1490","scopus_import":"1","isi":1,"month":"05","year":"2023","article_processing_charge":"No","publication_identifier":{"issn":["1350-7265"]},"date_published":"2023-05-01T00:00:00Z","oa_version":"Preprint","author":[{"full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","orcid":"0000-0001-5366-9603","last_name":"Erdös"},{"full_name":"Xu, Yuanyuan","id":"7902bdb1-a2a4-11eb-a164-c9216f71aea3","first_name":"Yuanyuan","orcid":"0000-0003-1559-1205","last_name":"Xu"}],"type":"journal_article","_id":"12707","intvolume":"        29","publication_status":"published","external_id":{"arxiv":["2112.12093 "],"isi":["000947270100008"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2112.12093"}],"status":"public","day":"01","ec_funded":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_type":"original","issue":"2","project":[{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"quality_controlled":"1","date_updated":"2024-10-09T21:04:45Z","title":"Small deviation estimates for the largest eigenvalue of Wigner matrices","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"}],"corr_author":"1","volume":29,"arxiv":1,"citation":{"ista":"Erdös L, Xu Y. 2023. Small deviation estimates for the largest eigenvalue of Wigner matrices. Bernoulli. 29(2), 1063–1079.","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>","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>.","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."},"publication":"Bernoulli","publisher":"Bernoulli Society for Mathematical Statistics and Probability"}