Large Deviations Asymptotics of Rectangular Spherical Integral

Published 14 Jun 2021 in math.PR | (2106.07146v1)

Abstract: In this article we study the Dyson Bessel process, which describes the evolution of singular values of rectangular matrix Brownian motions, and prove a large deviation principle for its empirical particle density. We then use it to obtain the asymptotics of the so-called rectangular spherical integrals as $m,n$ go to infinity while $m/n$ converges.

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