{"article_type":"original","publication_identifier":{"issn":["0022-2488"]},"year":"2024","article_number":"063302","language":[{"iso":"eng"}],"volume":65,"quality_controlled":"1","publisher":"AIP Publishing","date_created":"2024-08-04T22:01:22Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_published":"2024-06-01T00:00:00Z","oa_version":"Preprint","publication_status":"published","doi":"10.1063/5.0209705","date_updated":"2025-04-14T07:57:18Z","type":"journal_article","arxiv":1,"abstract":[{"lang":"eng","text":"We consider the spectral radius of a large random matrix X with independent, identically distributed entries. We show that its typical size is given by a precise three-term asymptotics with an optimal error term beyond the radius of the celebrated circular law. The coefficients in this asymptotics are universal but they differ from a similar asymptotics recently proved for the rightmost eigenvalue of X in Cipolloni et al., Ann. Probab. 51(6), 2192–2242 (2023). To access the more complicated spectral radius, we need to establish a new decorrelation mechanism for the low-lying singular values of X − z for different complex shift parameters z using the Dyson Brownian Motion."}],"citation":{"ista":"Cipolloni G, Erdös L, Xu Y. 2024. Precise asymptotics for the spectral radius of a large random matrix. Journal of Mathematical Physics. 65(6), 063302.","ieee":"G. Cipolloni, L. Erdös, and Y. Xu, “Precise asymptotics for the spectral radius of a large random matrix,” <i>Journal of Mathematical Physics</i>, vol. 65, no. 6. AIP Publishing, 2024.","short":"G. Cipolloni, L. Erdös, Y. Xu, Journal of Mathematical Physics 65 (2024).","mla":"Cipolloni, Giorgio, et al. “Precise Asymptotics for the Spectral Radius of a Large Random Matrix.” <i>Journal of Mathematical Physics</i>, vol. 65, no. 6, 063302, AIP Publishing, 2024, doi:<a href=\"https://doi.org/10.1063/5.0209705\">10.1063/5.0209705</a>.","ama":"Cipolloni G, Erdös L, Xu Y. Precise asymptotics for the spectral radius of a large random matrix. <i>Journal of Mathematical Physics</i>. 2024;65(6). doi:<a href=\"https://doi.org/10.1063/5.0209705\">10.1063/5.0209705</a>","apa":"Cipolloni, G., Erdös, L., &#38; Xu, Y. (2024). Precise asymptotics for the spectral radius of a large random matrix. <i>Journal of Mathematical Physics</i>. AIP Publishing. <a href=\"https://doi.org/10.1063/5.0209705\">https://doi.org/10.1063/5.0209705</a>","chicago":"Cipolloni, Giorgio, László Erdös, and Yuanyuan Xu. “Precise Asymptotics for the Spectral Radius of a Large Random Matrix.” <i>Journal of Mathematical Physics</i>. AIP Publishing, 2024. <a href=\"https://doi.org/10.1063/5.0209705\">https://doi.org/10.1063/5.0209705</a>."},"ec_funded":1,"status":"public","day":"01","article_processing_charge":"No","author":[{"full_name":"Cipolloni, Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992","first_name":"Giorgio","last_name":"Cipolloni"},{"first_name":"László","last_name":"Erdös","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Yuanyuan","last_name":"Xu","full_name":"Xu, Yuanyuan","id":"7902bdb1-a2a4-11eb-a164-c9216f71aea3","orcid":"0000-0003-1559-1205"}],"issue":"6","intvolume":"        65","oa":1,"publication":"Journal of Mathematical Physics","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"_id":"17375","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2210.15643","open_access":"1"}],"month":"06","title":"Precise asymptotics for the spectral radius of a large random matrix","acknowledgement":"L.E. and Y.X. were supported by the ERC Advanced Grant “RMTBeyond” Grant No. 101020331.","department":[{"_id":"LaEr"}],"corr_author":"1","scopus_import":"1","external_id":{"arxiv":["2210.15643"]}}