On Resolvent Identities in Gaussian Ensembles at the Edge of the Spectrum

TL;DR

This paper derives recursive identities for joint moments of resolvent traces in Gaussian random matrix ensembles at spectral edges, providing insights into their spectral behavior and potential extensions to non-Gaussian cases.

Contribution

It introduces recursive identities for resolvent trace moments at spectral edges in Gaussian ensembles, advancing understanding of their spectral properties.

Findings

Recursive identities for resolvent moments at spectral edges

Discussion on extending results to non-Gaussian ensembles

Insights into spectral edge behavior of Gaussian matrices

Abstract

We obtain the recursive identities for the joint moments of the traces of the powers of the resolvent for Gaussian ensembles of random matrices at the soft and hard edges of the spectrum. We also discuss the possible ways to extend these results to the non-Gaussian case.