Non-Hermitian Random Matrix Ensembles

TL;DR

This paper reviews non-Hermitian random matrix ensembles, focusing on Ginibre ensembles and their elliptic deformations, analyzing eigenvalue correlations in different non-Hermitian limits.

Contribution

It provides a comprehensive review of eigenvalue correlations in non-Hermitian ensembles, including exact reductions and limit analyses.

Findings

Eigenvalue correlations are exactly expressed via two-point kernels.

Analysis of eigenvalue behavior in strongly and weakly non-Hermitian limits.

Discussion of elliptic deformations of Ginibre ensembles.

Abstract

This is a concise review of the complex, real and quaternion real Ginibre random matrix ensembles and their elliptic deformations. Eigenvalue correlations are exactly reduced to two-point kernels and discussed in the strongly and weakly non-Hermitian limits of large matrix size.