On the proof of universality for orthogonal and symplectic ensembles in random matrix theory

TL;DR

This paper provides a simplified proof of universality in orthogonal and symplectic random matrix ensembles, offering new asymptotic insights into partition functions for different beta values.

Contribution

It introduces a streamlined proof of a key result for universality in orthogonal and symplectic ensembles, enhancing understanding of partition function ratios.

Findings

Asymptotic information on beta=1,2,4 partition functions

Streamlined proof of a crucial universality result

Implications for bulk and edge universality in random matrices

Abstract

We give a streamlined proof of a quantitative version of a result from [DG1] which is crucial for the proof of universality in the bulk [DG1] and also at the edge [DG2] for orthogonal and symplectic ensembles of random matrices. As a byproduct, this result gives asymptotic information on a certain ratio of the beta=1,2,4 partition functions for log gases.