Title: Multivariate normal approximation for traces of random unitary matrices
Speaker: Gaultier Lambert
Abstract: Let us consider a random matrix U of size n distributed according to the Haar measure on the unitary group. It is well-known that for any k≥1, Tr[U^k] converges as n tends to infinity to a Gaussian random variable and that, surprisingly, the speed of convergence is super exponential. In this talk, we revisit this problem and present non asymptotic bounds for the total variation distance between Tr[U^k] and a Gaussian. We will also consider the multivariate problem and explain how this affect the rate of convergence. We expect that our bounds are almost optimal. This is joint work with Kurt Johansson (KTH).