Asymptotics of unitary and othogonal matrix integrals

Details Asymptotics of unitary and othogonal matrix integrals Asymptotics of unitary and othogonal matrix integrals

2006-08-08

arxiv.org/abs/math/0608193v3

Mathematics

Probability

41 pages, important modifications, new section about orthogonal integrals

Scientific paper

In this paper, we prove that in small parameter regions, arbitrary unitary matrix integrals converge in the large $N$ 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.

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