Random matrix ensembles: Wang-Landau algorithm for spectral densities

TL;DR

This paper introduces a Wang-Landau algorithm-based method for efficiently computing spectral densities and thermodynamic properties of random matrix ensembles, offering an effective alternative to traditional Monte Carlo techniques.

Contribution

The paper presents a novel application of the Wang-Landau algorithm to random matrix spectral density estimation, enhancing computational efficiency and versatility for beta-ensembles.

Findings

Successfully computes spectral densities for various ensembles

Enables simultaneous analysis of spectral and thermodynamic properties

Outperforms traditional Monte Carlo methods in efficiency

Abstract

We propose a method based on the Wang-Landau algorithm to numerically generate the spectral densities of random matrix ensembles. The method employs Dyson's log-gas formalism for random matrix eigenvalues and also enables one to simultaneously investigate the thermodynamic properties. This approach is a powerful alternative to the conventionally used Monte Carlo simulations based on the Boltzmann sampling, and is ideally suited for investigating beta-ensembles.