Asymptotics of k dimensional spherical integrals and applications

Alice Guionnet; Jonathan Husson

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arXiv · 2101.01983

Asymptotics of k dimensional spherical integrals and applications

Alice Guionnet·Jonathan Husson

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Abstract

In this article, we prove that k-dimensional spherical integrals are asymptotically equivalent to the product of 1-dimensional spherical integrals. This allows us to generalize several large deviations principles in random matrix theory known before only in a one-dimensional case. As examples, we study the universality of the large deviations for k extreme eigenvalues of Wigner matrices (resp. Wishart matrices, resp. matrices with general variance profiles) with sharp sub-Gaussian entries, as well as large deviations principles for extreme eigenvalues of Gaussian Wigner and Wishart matrices with a finite dimensional perturbation.

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Alice Guionnet, Jonathan Husson. 2021-01-06. Asymptotics of k dimensional spherical integrals and applications. https://arxiv.org/abs/2101.01983

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