Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Erdős, László, Lee, Jaehun
Institution: Institute of Science and Technology Austria
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7167714293