Asymptotics of k dimensional spherical integrals and applications
Probability
2023-04-12 v2
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.
Cite
@article{arxiv.2101.01983,
title = {Asymptotics of k dimensional spherical integrals and applications},
author = {Alice Guionnet and Jonathan Husson},
journal= {arXiv preprint arXiv:2101.01983},
year = {2023}
}