On the Gaussian Random Matrix Ensembles with Additional Symmetry Conditions

TL;DR

This paper investigates how additional symmetry conditions in Gaussian unitary random matrix ensembles influence their limiting spectral distributions and correlation functions.

Contribution

It introduces symmetry conditions into Gaussian unitary ensembles and analyzes their impact on spectral measures and correlations.

Findings

Symmetry conditions alter the limiting spectral measures.

Correlation functions are affected by the additional symmetries.

Results provide new insights into structured random matrix ensembles.

Abstract

The Gaussian unitary random matrix ensembles satisfying some additional symmetry conditions are considered. The effect of these conditions on the limiting normalized counting measures and correlation functions is studied.