{"license":"https://creativecommons.org/licenses/by-nc-nd/4.0/","article_processing_charge":"Yes (via OA deal)","tmp":{"image":"/images/cc_by_nc_nd.png","legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","short":"CC BY-NC-ND (4.0)","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)"},"abstract":[{"lang":"eng","text":"We consider N×N non-Hermitian random matrices of the form X+A, where A is a general deterministic matrix and N−−√X consists of independent entries with zero mean, unit variance, and bounded densities. For this ensemble, we prove (i) a Wegner estimate, i.e. that the local density of eigenvalues is bounded by N1+o(1) and (ii) that the expected condition number of any bulk eigenvalue is bounded by N1+o(1); both results are optimal up to the factor No(1). The latter result complements the very recent matching lower bound obtained in [15] (arXiv:2301.03549) and improves the N-dependence of the upper bounds in [5,6,32] (arXiv:1906.11819, arXiv:2005.08930, arXiv:2005.08908). Our main ingredient, a near-optimal lower tail estimate for the small singular values of X+A−z, is of independent interest."}],"year":"2024","title":"Wegner estimate and upper bound on the eigenvalue condition number of non-Hermitian random matrices","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"date_created":"2024-05-12T22:01:02Z","main_file_link":[{"url":"https://doi.org/10.1002/cpa.22201","open_access":"1"}],"ec_funded":1,"type":"journal_article","has_accepted_license":"1","oa":1,"ddc":["510"],"article_type":"original","month":"05","author":[{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","last_name":"Erdös","orcid":"0000-0001-5366-9603","first_name":"László"},{"id":"dd216c0a-c1f9-11eb-beaf-e9ea9d2de76d","full_name":"Ji, Hong Chang","last_name":"Ji","first_name":"Hong Chang"}],"publication":"Communications on Pure and Applied Mathematics","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","language":[{"iso":"eng"}],"scopus_import":"1","day":"03","quality_controlled":"1","_id":"15378","status":"public","citation":{"mla":"Erdös, László, and Hong Chang Ji. “Wegner Estimate and Upper Bound on the Eigenvalue Condition Number of Non-Hermitian Random Matrices.” <i>Communications on Pure and Applied Mathematics</i>, Wiley, 2024, doi:<a href=\"https://doi.org/10.1002/cpa.22201\">10.1002/cpa.22201</a>.","short":"L. Erdös, H.C. Ji, Communications on Pure and Applied Mathematics (2024).","ama":"Erdös L, Ji HC. Wegner estimate and upper bound on the eigenvalue condition number of non-Hermitian random matrices. <i>Communications on Pure and Applied Mathematics</i>. 2024. doi:<a href=\"https://doi.org/10.1002/cpa.22201\">10.1002/cpa.22201</a>","ista":"Erdös L, Ji HC. 2024. Wegner estimate and upper bound on the eigenvalue condition number of non-Hermitian random matrices. Communications on Pure and Applied Mathematics.","ieee":"L. Erdös and H. C. Ji, “Wegner estimate and upper bound on the eigenvalue condition number of non-Hermitian random matrices,” <i>Communications on Pure and Applied Mathematics</i>. Wiley, 2024.","chicago":"Erdös, László, and Hong Chang Ji. “Wegner Estimate and Upper Bound on the Eigenvalue Condition Number of Non-Hermitian Random Matrices.” <i>Communications on Pure and Applied Mathematics</i>. Wiley, 2024. <a href=\"https://doi.org/10.1002/cpa.22201\">https://doi.org/10.1002/cpa.22201</a>.","apa":"Erdös, L., &#38; Ji, H. C. (2024). Wegner estimate and upper bound on the eigenvalue condition number of non-Hermitian random matrices. <i>Communications on Pure and Applied Mathematics</i>. Wiley. <a href=\"https://doi.org/10.1002/cpa.22201\">https://doi.org/10.1002/cpa.22201</a>"},"acknowledgement":"László Erdős is partially supported by ERC Advanced Grant “RMTBeyond” No. 101020331. Hong Chang Ji is supported by ERC Advanced Grant “RMTBeyond” No. 101020331.","department":[{"_id":"LaEr"}],"publication_identifier":{"issn":["0010-3640"],"eissn":["1097-0312"]},"oa_version":"Published Version","publication_status":"epub_ahead","external_id":{"arxiv":["2301.04981"]},"doi":"10.1002/cpa.22201","date_published":"2024-05-03T00:00:00Z","publisher":"Wiley","date_updated":"2024-05-13T12:44:35Z"}