Large Deviations Asymptotics of Rectangular Spherical Integral

2021/06/14 by Guionnet, Alice, Huang, Jiaoyang
#60B20 #60F10 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2106.07146

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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