Large Deviations Asymptotics of Rectangular Spherical Integral

Alice Guionnet; Jiaoyang Huang

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arXiv · 2106.07146

Large Deviations Asymptotics of Rectangular Spherical Integral

Alice Guionnet·Jiaoyang Huang

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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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Alice Guionnet, Jiaoyang Huang. 2021-06-14. Large Deviations Asymptotics of Rectangular Spherical Integral. https://arxiv.org/abs/2106.07146

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