Asymptotics of unitary and othogonal matrix integrals
Probability
2019-02-27 v3
Abstract
In this paper, we prove that in small parameter regions, arbitrary unitary matrix integrals converge in the large limit and match their formal expansion. Secondly we give a combinatorial model for our matrix integral asymptotics and investigate examples related to free probability and the HCIZ integral. Our convergence result also leads us to new results of smoothness of microstates. We finally generalize our approach to integrals over the othogonal group.
Cite
@article{arxiv.math/0608193,
title = {Asymptotics of unitary and othogonal matrix integrals},
author = {Benoit Collins and Alice Guionnet and Edouard Maurel-Segala},
journal= {arXiv preprint arXiv:math/0608193},
year = {2019}
}
Comments
41 pages, important modifications, new section about orthogonal integrals