Mesoscopic eigenvalue statistics for correlated random matrices

László Erdős; Jaehun Lee

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arXiv · 2607.05848

Mesoscopic eigenvalue statistics for correlated random matrices

László Erdős·Jaehun Lee

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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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László Erdős, Jaehun Lee. 2026-07-07. Mesoscopic eigenvalue statistics for correlated random matrices. https://arxiv.org/abs/2607.05848

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