On the moments of characteristic polynomials

TL;DR

This paper investigates the asymptotic behavior of moments of characteristic polynomials in large Hermitian random matrices, especially the Gaussian Unitary Ensemble, using a novel analytical approach.

Contribution

It introduces a new method for deriving asymptotic formulas for moments, revealing subtle structural details previously unnoticed.

Findings

Asymptotic formulas for moments of characteristic polynomials are derived.

The approach uncovers subtle structural features in the moments.

Results are primarily focused on the Gaussian Unitary Ensemble, with implications for other Hermitian ensembles.

Abstract

We examine the asymptotics of the moments of characteristic polynomials of $N\times N$ matrices drawn from the Hermitian ensembles of Random Matrix Theory, in the limit as $N\to\infty$. We focus in particular on the Gaussian Unitary Ensemble, but discuss other Hermitian ensembles as well. We employ a novel approach to calculate asymptotic formulae for the moments, enabling us to uncover subtle structure not apparent in previous approaches.