Singular-values of matrix-valued Ornstein-Uhlenbeck processes

摘要

The system of singular-values of a square matrix whose components are independent Ornstein-Uhlenbeck processes corresponds to a diffusion model of interacting particles. We show that the weak limit, as the dimension of the matrix tends to infinity, of the associated empirical measure process is a deterministic measure-valued process and converges to a fixed law as the time t tends to infinity.