A convergent $1/n$-expansion for GSE and GOE

TL;DR

This paper extends asymptotic expansion results from GUE to all Gaussian ensembles, deriving differential equations and explicit formulas for densities and moment generating functions.

Contribution

It provides a unified approach to asymptotic expansions across all Gaussian ensembles, including explicit formulas and differential equations.

Findings

Derived differential equations for densities and moment generating functions.

Calculated explicit expressions for moment generating functions.

Extended asymptotic expansion results from GUE to all Gaussian ensembles.

Abstract

We generalize the results on the asymptotic expansion from Gaussian Unitary Ensembles case to all Gaussian Ensembles. We derive differential equations on densities and their moment generating functions for all Gaussian Ensembles. Also, we calculate explicit expressions for the moment generating functions for all Gaussian Ensembles.