A generalized ensemble of random matrices

TL;DR

This paper introduces a new random matrix ensemble that combines GUE and Poisson statistics, modeled as noninteracting fermions at finite temperature, maintaining $U(N)$ invariance.

Contribution

It proposes a generalized ensemble unifying GUE and Poisson statistics with a fermionic system analogy, expanding the understanding of random matrix models.

Findings

The ensemble respects $U(N)$ invariance.

It is equivalent to a system of noninteracting, confined fermions.

The model bridges GUE and Poisson level statistics.

Abstract

A random matrix ensemble incorporating both GUE and Poisson level statistics while respecting $U(N)$ invariance is proposed and shown to be equivalent to a system of noninteracting, confined, one dimensional fermions at finite temperature.