Perturbations of diagonal matrices by band random matrices

TL;DR

This paper derives an explicit formula for the spectral density of large diagonal matrices perturbed by symmetric Gaussian matrices with a specified variance profile.

Contribution

It provides a new explicit spectral density formula for large diagonal matrices perturbed by band Gaussian matrices, extending previous results.

Findings

Explicit spectral density formula derived

Applicable to matrices with small variance profiles

Enhances understanding of spectral behavior under perturbations

Abstract

We exhibit an explicit formula for the spectral density of a (large) random matrix which is a diagonal matrix whose spectral density converges, perturbated by the addition of a symmetric matrix with Gaussian entries and a given (small) limiting variance profile.