Mesoscopic eigenvalue statistics for Wigner-type matrices
Probability
2023-01-05 v1
Abstract
We prove a universal mesoscopic central limit theorem for linear eigenvalue statistics of a Wigner-type matrix inside the bulk of the spectrum with compactly supported twice continuously differentiable test functions. The main novel ingredient is an optimal local law for the two-point function and a general class of related quantities involving two resolvents at nearby spectral parameters.
Cite
@article{arxiv.2301.01712,
title = {Mesoscopic eigenvalue statistics for Wigner-type matrices},
author = {Volodymyr Riabov},
journal= {arXiv preprint arXiv:2301.01712},
year = {2023}
}