Edge Universality for Orthogonal Ensembles of Random Matrices

TL;DR

This paper proves that the local eigenvalue statistics at the spectrum edge are universal for orthogonal invariant random matrix ensembles with real analytic potentials, extending known universality results.

Contribution

It establishes edge universality for orthogonal ensembles using a representation of kernels in terms of unitary ensemble kernels, building on prior work.

Findings

Edge universality holds for orthogonal ensembles with real analytic potentials.

The representation of kernels links orthogonal and unitary ensembles.

Results apply to spectra with one interval limiting support.

Abstract

We prove edge universality of local eigenvalue statistics for orthogonal invariant matrix models with real analytic potentials and one interval limiting spectrum. Our starting point is the result of \cite{S:08} on the representation of the reproducing matrix kernels of orthogonal ensembles in terms of scalar reproducing kernel of corresponding unitary ensemble.