Orthogonal and symplectic matrix models: universality and other properties

TL;DR

This paper investigates orthogonal and symplectic matrix models with polynomial potentials, establishing convergence rates, variance bounds, partition function asymptotics, and proving local eigenvalue statistics universality in the bulk.

Contribution

It extends universality results and asymptotic analysis to orthogonal and symplectic matrix models with polynomial potentials and multi-interval supports.

Findings

Established bounds for convergence rates of eigenvalue statistics

Derived variance bounds for linear eigenvalue statistics

Proved universality of local eigenvalue statistics in the bulk

Abstract

We study orthogonal and symplectic matrix models with polynomial potentials and multi interval supports of the equilibrium measure. For these models we find the bounds (similar to the case of hermitian matrix models) for the rate of convergence of linear eigenvalue statistics and for the variance of linear eigenvalue statistics and find the logarithms of partition functions up to the order O(1). We prove also universality of local eigenvalue statistics in the bulk.