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Asymptotics of unitary and orthogonal matrix integrals (2009)
by
Benoît Collins
,
Alice Guionnet
,
Edouard Maurel-segala
| Citations: | 10 - 3 self |
BibTeX
@MISC{Collins09asymptoticsof,
author = {Benoît Collins and Alice Guionnet and Edouard Maurel-segala},
title = {Asymptotics of unitary and orthogonal matrix integrals},
year = {2009}
}
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Abstract
Abstract. 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.
