On the edge universality of the local eigenvalue statistics of matrix models

TL;DR

This paper proves that the local eigenvalue statistics near the edges of the spectrum in certain matrix models are universal, independent of the specific potential, under real analytic conditions and support configurations.

Contribution

It establishes edge universality for local eigenvalue statistics in unitary invariant matrix models using a $1/n$-expansion approach.

Findings

Eigenvalue statistics near spectral edges are universal.

Universality holds for real analytic potentials with one or two support intervals.

The results extend to cases with disjoint spectral supports.

Abstract

Basing on our recent results on the $1/n$-expansion in unitary invariant random matrix ensembles, known as matrix models, we prove that the local eigenvalue statistic, arising in a certain neighborhood of the edges of the support of the Density of States, is independent of the form of the potential, determining the matrix model. Our proof is applicable to the case of real analytic potentials and of supports, consisting of one or two disjoint intervals.