Single eigenvalue fluctuations of general Wigner-type matrices
Abstract
We consider the single eigenvalue fluctuations of random matrices of general Wigner-type, under a one-cut assumption on the density of states. For eigenvalues in the bulk, we prove that the asymptotic fluctuations of a single eigenvalue around its classical location are Gaussian with a universal variance. Our method is based on a dynamical approach to mesoscopic linear spectral statistics which reduces their behavior on short scales to that on larger scales. We prove a central limit theorem for linear spectral statistics on larger scales via resolvent techniques and show that for certain classes of test functions, the leading-order contribution to the variance agrees with the GOE/GUE cases.
Cite
@article{arxiv.2105.01178,
title = {Single eigenvalue fluctuations of general Wigner-type matrices},
author = {Benjamin Landon and Patrick Lopatto and Philippe Sosoe},
journal= {arXiv preprint arXiv:2105.01178},
year = {2022}
}
Comments
v4: incorporated referee comments, v3: paper re-organized, v2: corrected misprints, improved presentation