Decomposition of spectral density in individual eigenvalue contributions

TL;DR

This paper decomposes the spectral density of Wigner and Wishart random matrices into individual eigenvalue contributions, showing that eigenvalue fluctuations are approximately normally distributed for medium-sized matrices.

Contribution

It introduces a method to decompose spectral densities into individual eigenvalue contributions and demonstrates the normality of eigenvalue fluctuations in medium-sized matrices.

Findings

Eigenvalue fluctuations are nearly normal for medium matrix sizes.

Spectral densities can be decomposed into individual eigenvalue contributions.

The approach applies to Wigner and Wishart ensembles.

Abstract

The eigenvalue densities of two random matrix ensembles, the Wigner Gaussian matrices and the Wishart covariant matrices, are decomposed in the contributions of each individual eigenvalue distribution. It is shown that the fluctuations of all eigenvalues, for medium matrix sizes, are described with a good precision by nearly normal distributions.