Random walkers versus random crowds: diffusion of large matrices

TL;DR

This paper explores the spectral properties of large matrices undergoing stochastic diffusion, revealing unexpected connections between different matrix ensembles and their spectral behaviors.

Contribution

It introduces a novel link between the spectral properties of matrix-valued multiplicative diffusion processes for hermitian and unitary ensembles.

Findings

Established a surprising connection between spectral properties of hermitian and unitary matrix ensembles.

Provided insights into the diffusion processes of large matrices in the context of free probability.

Reviewed the application of random matrix theory to stochastic diffusion processes.

Abstract

We briefly review the random matrix theory for large N by N matrices viewed as free random variables in a context of stochastic diffusion. We establish a surprising link between the spectral properties of matrix-valued multiplicative diffusion processes for hermitian and unitary ensembles.