Product of Non-Hermitian Random Matrices

TL;DR

This paper studies the eigenvalue distribution of the product of multiple independent non-Hermitian elliptic random matrices, revealing a determinantal point process structure for their eigenvalues.

Contribution

It derives the joint eigenvalue distribution for the product of elliptic non-Hermitian matrices, a novel result in random matrix theory.

Findings

Eigenvalues form a determinantal point process

Joint eigenvalue distribution derived for product matrices

Extends understanding of non-Hermitian matrix products

Abstract

We investigate the product of $n$ complex non-Hermitian, independent random matrices, each of size $N\times N$ in the class of elliptic matrices, with independent identically distributed entries. The joint probability distribution of the complex eigenvalues of the product matrix is found to be given by a determinantal point process.