Non-universality of compact support probability distributions in random matrix theory

TL;DR

This paper investigates the differences in two-point resolvent functions between generalized fixed/bounded trace ensembles and the Gaussian ensemble, revealing non-universality and specific explicit discrepancies.

Contribution

It demonstrates the non-universality of the two-point resolvent in certain ensembles and proves the large-n equivalence of all k-point resolvents despite this non-universality.

Findings

Two-point resolvent differs from Gaussian ensemble by a non-universal part.

All k-point resolvents agree in the large-n limit across ensembles.

Explicit form of non-universal part for monomial potentials.

Abstract

The two-point resolvent is calculated in the large-n limit for the generalized fixed and bounded trace ensembles. It is shown to disagree with the one of the canonical Gaussian ensemble by a non-universal part which is given explicitly for all monomial potentials $V(M)=M^{2p}$. Moreover, we prove that for the generalized fixed and bounded trace ensemble all k-point resolvents agree in the large-n limit, despite their non-universality.