Mesoscopic eigenvalue statistics for correlated random matrices
Probability
2026-07-07 v1
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.
Cite
@article{arxiv.2607.05848,
title = {Mesoscopic eigenvalue statistics for correlated random matrices},
author = {László Erdős and Jaehun Lee},
journal= {arXiv preprint arXiv:2607.05848},
year = {2026}
}
Comments
44 pages