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

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.

arXiv comment9 pages

References in corpus (3)

• Correlation Functions, Cluster Functions and Spacing Distributions for Random Matrices
• Universality at the edge of the spectrum for unitary, orthogonal and symplectic ensembles of random matrices
• Asymptotics of the partition function for random matrices via Riemann-Hilbert techniques, and applications to graphical enumeration

Cited by in corpus (2)

• Lectures on random matrix models. The Riemann-Hilbert approach
• Universality for orthogonal and symplectic Laguerre-type ensembles