Central limit theorems for eigenvalues of deformations of Wigner matrices

TL;DR

This paper investigates how the fluctuations of the largest eigenvalues in deformed Wigner matrices depend on the perturbation's eigenvectors, identifying conditions for universal or non-universal behavior.

Contribution

It provides a detailed analysis of the conditions affecting the universality of eigenvalue fluctuations in deformed Wigner matrices.

Findings

Dependence of eigenvalue fluctuations on perturbation eigenvectors

Conditions leading to universality or non-universality

General situations affecting fluctuation behavior

Abstract

In this paper, we explain the dependance of the fluctuations of the largest eigenvalues of a Deformed Wigner model with respect to the eigenvectors of the perturbation matrix. We exhibit quite general situations that will give rise to universality or non universality of the fluctuations.