Stein's method, Markov processes, and linear eigenvalue statistics of random matrices
Probability
2025-10-01 v1
Abstract
We show how the infinitesimal exchangeable pairs approach to Stein's method combines naturally with the theory of Markov semigroups. We present a multivariate normal approximation theorem for functions of a random variable invariant with respect to a Markov semigroup. This theorem provides a Wasserstein distance bound in terms of quantities related to the infinitesimal generator of the semigroup. As an application, we deduce a rate of convergence for Johansson's celebrated theorem on linear eigenvalue statistics of Gaussian random matrix ensembles.
Cite
@article{arxiv.2509.25451,
title = {Stein's method, Markov processes, and linear eigenvalue statistics of random matrices},
author = {David Grzybowski and Mark Meckes},
journal= {arXiv preprint arXiv:2509.25451},
year = {2025}
}