On the computation of density and two-point correlation functions of a class of random matrix ensembles

TL;DR

This paper introduces a numerical method for computing density and two-point correlation functions in a broad class of random matrix ensembles, including new results for less-studied ensembles.

Contribution

It presents a versatile numerical approach applicable to complex random matrix models with biorthogonal interactions and arbitrary potentials, extending analysis to new ensembles.

Findings

Reproduced known results for classical ensembles

Obtained new numerical results for Muttalib-Borodin ensembles

Provided initial insights into the $oldsymbol{ extgamma}$-ensemble

Abstract

We demonstrate a method to solve a general class of random matrix ensembles numerically. The method is suitable for solving log-gas models with biorthogonal type two-body interactions and arbitrary potentials. We reproduce standard results for a variety of well-known ensembles and show some new results for the Muttalib-Borodin ensembles and recently introduced $\gamma$-ensemble for which analytic results are not yet available.