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Seminar
FIELD Mathematics
DATE November 10 (Wed), 2021
TIME 17:00-18:00
PLACE Online
SPEAKER Simm, Nicholas
HOST Lee, Jaehun
INSTITUTE University of Sussex
TITLE [GS_M_APP] Fluctuations and correlations for products of real asymmetric random matrices
ABSTRACT Consider a finite product of real asymmetric N x N random matrices with i.i.d. Gaussian entries. Recently, Forrester and Ipsen obtained finite-N formulae for the correlation functions of the real eigenvalues of such products in terms of a Pfaffian point process. I will discuss recent work where we obtain asymptotic estimates for the correlation kernel of the process as N tends to infinity, in particular establishing universality of the real eigenvalues in the bulk and spectral edge regimes. I will explain how we apply such estimates to prove central limit theorems for linear statistics and to establish universality of the largest real eigenvalue. Joint work with Will FitzGerald (University of Manchester).
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