{"page":"3785-3840","date_created":"2024-05-12T22:01:02Z","oa":1,"doi":"10.1002/cpa.22201","department":[{"_id":"LaEr"}],"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1097-0312"],"issn":["0010-3640"]},"article_processing_charge":"Yes (via OA deal)","file_date_updated":"2025-01-09T09:36:41Z","scopus_import":"1","year":"2024","month":"09","date_published":"2024-09-01T00:00:00Z","_id":"15378","intvolume":"        77","type":"journal_article","oa_version":"Published Version","ddc":["510"],"OA_place":"publisher","author":[{"full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","first_name":"László","last_name":"Erdös"},{"id":"dd216c0a-c1f9-11eb-beaf-e9ea9d2de76d","full_name":"Ji, Hong Chang","last_name":"Ji","first_name":"Hong Chang"}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode","image":"/images/cc_by_nc_nd.png","name":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","short":"CC BY-NC-ND (4.0)"},"external_id":{"arxiv":["2301.04981"]},"publication_status":"published","OA_type":"hybrid","ec_funded":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","day":"01","project":[{"call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"date_updated":"2025-01-09T09:37:24Z","quality_controlled":"1","title":"Wegner estimate and upper bound on the eigenvalue condition number of non-Hermitian random matrices","has_accepted_license":"1","issue":"9","article_type":"original","file":[{"date_updated":"2025-01-09T09:36:41Z","date_created":"2025-01-09T09:36:41Z","checksum":"fbcc9cc7bf274f024e4f4afc9c208f96","content_type":"application/pdf","access_level":"open_access","file_id":"18803","success":1,"creator":"dernst","file_name":"2024_CommPureApplMath_Erdoes.pdf","file_size":566963,"relation":"main_file"}],"volume":77,"publication":"Communications on Pure and Applied Mathematics","publisher":"Wiley","arxiv":1,"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>, vol. 77, no. 9, Wiley, 2024, pp. 3785–840, doi:<a href=\"https://doi.org/10.1002/cpa.22201\">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>","short":"L. Erdös, H.C. Ji, Communications on Pure and Applied Mathematics 77 (2024) 3785–3840.","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>.","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>, vol. 77, no. 9. Wiley, pp. 3785–3840, 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;77(9):3785-3840. 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. 77(9), 3785–3840."},"corr_author":"1","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."}],"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."}