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Mesoscopic eigenvalue statistics for correlated random matrices
Abstract
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.
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BibTeX
@misc{erdos2026mesoscopic,
title = {{Mesoscopic eigenvalue statistics for correlated random matrices}},
author = {László Erdős and Jaehun Lee},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.05848},
eprint = {2607.05848},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.05848},
}
RIS
TY - UNPB
TI - Mesoscopic eigenvalue statistics for correlated random matrices
AU - László Erdős
AU - Jaehun Lee
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2607.05848
UR - https://arxiv.org/abs/2607.05848
AB - 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.
ER -