On Finite Rank Deformations of Wigner Matrices II: Delocalized Perturbations

TL;DR

This paper investigates how finite rank perturbations affect the spectrum of Wigner matrices, focusing on the distribution of outliers when the perturbation eigenvectors are delocalized, extending previous results to broader conditions.

Contribution

It extends existing results on outlier distributions in Wigner matrices to include delocalized perturbations with finite fourth moment entries.

Findings

Outliers' distribution characterized for delocalized eigenvectors.

Results applicable to matrices with finite fourth moments.

Generalization of prior work by Capitaine, Donati-Martin, and Féral.

Abstract

We study the distribution of the outliers in the spectrum of finite rank deformations of Wigner random matrices. We assume that the matrix entries have finite fourth moment and extend the results by Capitaine, Donati-Martin, and F\'eral for perturbations whose eigenvectors are delocalized.