Density of states for GUE, GOE, and interpolating ensembles through supersymmetric approach

TL;DR

This paper employs supersymmetric formalism to derive the density of states for GUE, GOE, and interpolating ensembles, providing new derivations of corrections to Wigner's law and extending previous work.

Contribution

It introduces a supersymmetric approach to analyze density of states for multiple ensembles, including interpolating ones, with new derivations of 1/N corrections.

Findings

Derived integral formula for GOE density of states

Provided saddle-point analysis for 1/N correction to Wigner's law

Extended methods to interpolating ensembles of Mehta--Pandey

Abstract

We use the supersymmetric formalism to derive an integral formula for the density of states of the Gaussian Orthogonal Ensemble, and then apply saddle-point analysis to give a new derivation of the 1/N-correction to Wigner's law. This extends the work of Disertori on the Gaussian Unitary Ensemble. We also apply our method to the interpolating ensembles of Mehta--Pandey.