Benjamin Landon (MIT)

Abstract. Dyson Brownian motion is a stochastic random matrix dynamics used in proofs of eigenvalue universality. We will briefly review the notion of universality in random matrix theory as well as the role played by Dyson Brownian motion in its study. We then focus on recent approaches to proving local ergodicity of Dyson Brownian motion, including coupling and homogenization techniques. This talk is based on joint work with P. Sosoe and H.-T. Yau.