Seminar Event Detail

Integrable Systems and Random Matrix Theory

Date:  Monday, April 11, 2022
Location:  ZOOM ID: 926 6491 9790 Virtual (4:00 PM to 5:00 PM)

Title:  Asymptotics of spherical integrals and large deviations of the largest eigenvalues for random matrices.

Abstract:   The Harish-Chandra-Itzykson-Zuber integral, also called spherical integral is defined as the expectation of exp(Tr(AUBU*)) for A and B two self adjoint matrices and U Haar-distributed on the unitary/orthogonal/symplectic group. It was initially introduced by Harish-Chandra to study Lie groups. Since then, it has known many kinds of applications, from physics to statistical learning. In this talk we will study the asymptotics of these integrals when one of the matrices remains of finite rank. We will also see how to derive from these asymptotics large deviation principles for the largest eigenvalues for random matrix models that satisfy a sub-Gaussian bound.

A recording of the talk can be found here.


Speaker:  Jonathan Husson
Institution:  University of Michigan

Event Organizer:   Ahmad Barhoumi


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