06/07/2022, 17:00 — 18:00 — Online
Gaultier Lambert, University of Zurich
Normal approximation for traces of random unitary matrices
This talk aims to report on the fluctuations of traces of powers of a random $n$ by $n$ matrix U distributed according to the Haar measure on the unitary group. This random matrix problem has been extensively studied using several different methods such as asymptotics of Toeplitz determinants, representation theory, loop equations etc. It turns out that for any $k≥1$, $Tr[U^k]$ converges as $n$ tends to infinity to a Gaussian random variable with a super exponential rate of convergence. In this talk, I will explain some of these results and present some recent work with Klara Courteaut and Kurt Johansson (KTH) in which we revisited this classical problem.
