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