[{"project":[{"grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020"}],"doi":"10.48550/arXiv.2607.05848","department":[{"_id":"LaEr"}],"title":"Mesoscopic eigenvalue statistics for correlated random matrices","publication_status":"submitted","year":"2026","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"07","author":[{"last_name":"Lee","id":"96155047-f36a-11ef-b766-8b5ae7cecd49","first_name":"Jaehun","full_name":"Lee, Jaehun"},{"first_name":"László","full_name":"Erdös, László","last_name":"Erdös","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"}],"das_tickbox":"1","date_published":"2026-07-07T00:00:00Z","arxiv":1,"article_processing_charge":"No","corr_author":"1","OA_place":"repository","_id":"22359","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."}],"type":"preprint","article_number":"2607.05848","language":[{"iso":"eng"}],"external_id":{"arxiv":["2607.05848"]},"month":"07","acknowledgement":"Supported by ERC Advanced Grant “RMTBeyond” No. 101020331","status":"public","keyword":["Central limit theorem","universality","matrix Dyson equation","multi-resolvent local law"],"date_updated":"2026-07-20T10:55:10Z","oa":1,"oa_version":"Preprint","ec_funded":1,"OA_type":"green","citation":{"ieee":"J. Lee and L. Erdös, “Mesoscopic eigenvalue statistics for correlated random matrices.” .","ama":"Lee J, Erdös L. Mesoscopic eigenvalue statistics for correlated random matrices. doi:<a href=\"https://doi.org/10.48550/arXiv.2607.05848\">10.48550/arXiv.2607.05848</a>","apa":"Lee, J., &#38; Erdös, L. (n.d.). Mesoscopic eigenvalue statistics for correlated random matrices. <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,” n.d. <a href=\"https://doi.org/10.48550/arXiv.2607.05848\">https://doi.org/10.48550/arXiv.2607.05848</a>.","ista":"Lee J, Erdös L. Mesoscopic eigenvalue statistics for correlated random matrices. 2607.05848.","short":"J. Lee, L. Erdös, (n.d.).","mla":"Lee, Jaehun, and László Erdös. <i>Mesoscopic Eigenvalue Statistics for Correlated Random Matrices</i>. 2607.05848, doi:<a href=\"https://doi.org/10.48550/arXiv.2607.05848\">10.48550/arXiv.2607.05848</a>."},"date_created":"2026-07-18T08:59:02Z","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2607.05848","open_access":"1"}]}]