Stochastic differential equations related to random matrix theory

TL;DR

This paper reviews recent advances in the mathematical understanding of infinite-dimensional stochastic differential equations that model interacting Brownian particles in continuous space, highlighting their existence and uniqueness properties.

Contribution

It synthesizes recent results on the existence and uniqueness of solutions to these complex stochastic systems, advancing theoretical understanding.

Findings

Established conditions for existence of solutions

Proved uniqueness of solutions under certain assumptions

Connected stochastic differential equations to random matrix theory

Abstract

In this note we review recent results on existence and uniqueness of solutions of infinite-dimensional stochastic differential equations describing interacting Brownian motions on $\R^d$.