{"OA_place":"repository","arxiv":1,"day":"01","type":"journal_article","intvolume":"        53","department":[{"_id":"LaEr"}],"oa":1,"issue":"6","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2404.17512","open_access":"1"}],"publisher":"Institute of Mathematical Statistics","status":"public","volume":53,"project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"date_updated":"2026-02-18T08:35:38Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2025","publication_identifier":{"issn":["0091-1798"],"eissn":["2168-894X"]},"page":"2256-2308","language":[{"iso":"eng"}],"acknowledgement":"The authors would like to thank the anonymous referee for providing helpful comments and suggestions. We also thank Joscha Henheik and Volodymyr Riabov for pointing out a gap in an earlier version of the proof of equation (3.18). The first, third, and fourth authors are supported by ERC Advanced Grant “RMTBeyond” No. 101020331.","doi":"10.1214/25-aop1761","publication_status":"published","OA_type":"green","date_created":"2026-02-17T07:58:20Z","_id":"21271","publication":"The Annals of Probability","title":"On the spectral edge of non-Hermitian random matrices","external_id":{"arxiv":["2404.17512"]},"date_published":"2025-11-01T00:00:00Z","corr_author":"1","article_processing_charge":"No","oa_version":"Preprint","author":[{"full_name":"Campbell, Andrew J","first_name":"Andrew J","id":"582b06a9-1f1c-11ee-b076-82ffce00dde4","last_name":"Campbell"},{"last_name":"Cipolloni","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio","full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992"},{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","first_name":"László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Hong Chang","full_name":"Ji, Hong Chang","last_name":"Ji","id":"dd216c0a-c1f9-11eb-beaf-e9ea9d2de76d"}],"article_type":"original","quality_controlled":"1","month":"11","ec_funded":1,"citation":{"chicago":"Campbell, Andrew J, Giorgio Cipolloni, László Erdös, and Hong Chang Ji. “On the Spectral Edge of Non-Hermitian Random Matrices.” <i>The Annals of Probability</i>. Institute of Mathematical Statistics, 2025. <a href=\"https://doi.org/10.1214/25-aop1761\">https://doi.org/10.1214/25-aop1761</a>.","ista":"Campbell AJ, Cipolloni G, Erdös L, Ji HC. 2025. On the spectral edge of non-Hermitian random matrices. The Annals of Probability. 53(6), 2256–2308.","ama":"Campbell AJ, Cipolloni G, Erdös L, Ji HC. On the spectral edge of non-Hermitian random matrices. <i>The Annals of Probability</i>. 2025;53(6):2256-2308. doi:<a href=\"https://doi.org/10.1214/25-aop1761\">10.1214/25-aop1761</a>","mla":"Campbell, Andrew J., et al. “On the Spectral Edge of Non-Hermitian Random Matrices.” <i>The Annals of Probability</i>, vol. 53, no. 6, Institute of Mathematical Statistics, 2025, pp. 2256–308, doi:<a href=\"https://doi.org/10.1214/25-aop1761\">10.1214/25-aop1761</a>.","ieee":"A. J. Campbell, G. Cipolloni, L. Erdös, and H. C. Ji, “On the spectral edge of non-Hermitian random matrices,” <i>The Annals of Probability</i>, vol. 53, no. 6. Institute of Mathematical Statistics, pp. 2256–2308, 2025.","short":"A.J. Campbell, G. Cipolloni, L. Erdös, H.C. Ji, The Annals of Probability 53 (2025) 2256–2308.","apa":"Campbell, A. J., Cipolloni, G., Erdös, L., &#38; Ji, H. C. (2025). On the spectral edge of non-Hermitian random matrices. <i>The Annals of Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/25-aop1761\">https://doi.org/10.1214/25-aop1761</a>"},"abstract":[{"lang":"eng","text":"For general non-Hermitian large random matrices X and deterministic deformation matrices A, we prove that the local eigenvalue statistics of A+X close to the typical edge points of its spectrum are universal. Furthermore, we show that, under natural assumptions, on A the spectrum of A+X does not have outliers at a distance larger than the natural fluctuation scale of the eigenvalues. As a consequence, the number of eigenvalues in each component of Spec(A+X) is deterministic."}]}