Hermitian and non-Hermitian perturbations of chiral Gaussian $\beta$-ensembles

TL;DR

This paper derives the joint eigenvalue distribution for rank one Hermitian and non-Hermitian perturbations of chiral Gaussian beta-ensembles, expanding understanding of spectral properties in random matrix theory.

Contribution

It provides the first explicit computation of joint eigenvalue distributions under rank one perturbations for these ensembles, covering both Hermitian and non-Hermitian cases.

Findings

Explicit joint eigenvalue distribution formulas derived.

Applicable to both Hermitian and non-Hermitian perturbations.

Enhances understanding of spectral behavior in perturbed chiral ensembles.

Abstract

We compute the joint eigenvalue distribution for the rank one Hermitian and non-Hermitian perturbations of chiral Gaussian $\beta$-ensembles ($\beta>0$) of random matrices.