Asymptotics of unitary and orthogonal matrix integrals

By Benoît Collins, Alice Guionnet, Édouard Maurel-Segala. 2006

56 citations recorded by the source corpus.

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 orthogonal group.

Subfields: Applied Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/f24b049e5a125f4b6774b3c1afb1805e4875293f