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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...
In this article, we set two analogous definitions of the free entropies χ and χ * introduced by Voiculescu (Invent. Math. 118 (1994) 411; 132 (1998) 189). We discuss their relations, improving the preceding results obtained in Cabanal-Duvillard and Guionnet (Ann. Probab. (2001), to appear), where a bound on the microstates entropy χ was established.
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