Combinatorics Seminar - Gaultier Lambert

November 19, 2019
Thursday, November 21, 2019 - 10:20am
Math Tower 154
Combinatorics Seminar

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).

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