Student Probability Seminar

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Rate of convergence of linear statistics of random Haar matrices

Speaker: Klara Courteaut, NYU Courant

Location: Warren Weaver Hall 202

Date: Wednesday, May 1, 2024, 12:30 p.m.

Synopsis:

We consider the convergence rate of the trace of powers of random matrices from the compact classical groups, including the CUE. We show that for high powers, the rate is close to the one obtained for the classical CLT - the Berry-Esseen theorem. This is expected because when the power is exactly equal to the dimension of the matrix, the eigenvalues are independent. However, the convergence is extremely fast for smaller powers: superexponential in total variation. Our results interpolate between these two cases.