[{"publication":"arXiv","author":[{"first_name":"Jaehun","last_name":"Lee","id":"96155047-f36a-11ef-b766-8b5ae7cecd49","full_name":"Lee, Jaehun"},{"orcid":"0000-0001-5366-9603","first_name":"László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László"}],"corr_author":"1","article_number":"2607.05848","title":"Mesoscopic eigenvalue statistics for correlated random matrices","oa":1,"type":"preprint","doi":"10.48550/arXiv.2607.05848","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2607.05848"}],"month":"07","publication_status":"submitted","language":[{"iso":"eng"}],"department":[{"_id":"LaEr"}],"project":[{"call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331"}],"article_processing_charge":"No","date_created":"2026-07-18T08:59:02Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","ec_funded":1,"abstract":[{"lang":"eng","text":"We prove a mesoscopic central limit theorem for linear eigenvalue statistics of correlated Hermitian random matrices. The class considered here includes Wigner and Wigner-type matrices, as well as models whose entry correlations decay polynomially in the distance between index pairs. The proof combines a multivariate cumulant expansion with multi-resolvent local laws and a detailed analysis of the resulting variance kernel on the operator-level."}],"date_updated":"2026-10-20T10:06:12Z","OA_place":"repository","date_published":"2026-07-07T00:00:00Z","OA_type":"green","keyword":["Central limit theorem","universality","matrix Dyson equation","multi-resolvent local law"],"fulldoi":"https://doi.org/10.48550/arXiv.2607.05848","arxiv":1,"das_tickbox":"1","day":"07","acknowledgement":"Supported by ERC Advanced Grant “RMTBeyond” No. 101020331","year":"2026","citation":{"ama":"Lee J, Erdös L. Mesoscopic eigenvalue statistics for correlated random matrices. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2607.05848\">10.48550/arXiv.2607.05848</a>","ista":"Lee J, Erdös L. Mesoscopic eigenvalue statistics for correlated random matrices. arXiv, 2607.05848.","ieee":"J. Lee and L. Erdös, “Mesoscopic eigenvalue statistics for correlated random matrices,” <i>arXiv</i>. .","apa":"Lee, J., &#38; Erdös, L. (n.d.). Mesoscopic eigenvalue statistics for correlated random matrices. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2607.05848\">https://doi.org/10.48550/arXiv.2607.05848</a>","chicago":"Lee, Jaehun, and László Erdös. “Mesoscopic Eigenvalue Statistics for Correlated Random Matrices.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2607.05848\">https://doi.org/10.48550/arXiv.2607.05848</a>.","mla":"Lee, Jaehun, and László Erdös. “Mesoscopic Eigenvalue Statistics for Correlated Random Matrices.” <i>ArXiv</i>, 2607.05848, doi:<a href=\"https://doi.org/10.48550/arXiv.2607.05848\">10.48550/arXiv.2607.05848</a>.","short":"J. Lee, L. Erdös, ArXiv (n.d.)."},"_id":"22359","status":"public","oa_version":"Preprint","external_id":{"arxiv":["2607.05848"]}}]