# Generalized random matrix model with additional interactions

## TL;DR

This paper introduces a generalized random matrix model with an extra interaction term, analyzing its equilibrium density through numerical solutions of a Riemann-Hilbert problem, revealing how the interaction modifies the confining potential.

## Contribution

The paper presents a new generalized random matrix ensemble incorporating an additional interaction parameter, expanding the understanding of such models.

## Key findings

- Equilibrium density computed numerically for the generalized model.
- The interaction parameter influences the effective confining potential.
- The model extends classical random matrix ensembles with a tunable interaction.

## Abstract

We introduce a log-gas model that is a generalization of a random matrix ensemble with an additional interaction, whose strength depends on a parameter $\gamma$. The equilibrium density is computed by numerically solving the Riemann-Hilbert problem associated with the ensemble. The effect of the additional parameter $\gamma$ associated with the two-body interaction can be understood in terms of an effective $\gamma$-dependent single-particle confining potential.