Workshop: Fluctuations for non-Hermitian dynamics

Speaker
Paul Bourgade, New-York University

Abstract
Rider and Virág proved that the characteristic polynomial of Ginibre random matrices converge to the Gaussian free field in the limit of large dimension. In this joint work with Giorgio Cipolloni and Jiaoyang Huang, we provide a dynamical extension out of equilibrium: Under the Brownian evolution on large non-Hermitian matrices the log-determinant converges to a 2+1 dimensional Gaussian field in the Edwards-Wilkinson regularity class.