Topological expansion of unitary integrals and maps
Résumé
I this article, we study integrals on the unitary group with respect to the Haar measure. We give a combinatorial interpretation in terms of maps of the asymptotic topological expansion, established previously by Guionnet and Novak. The maps we introduce-the maps of unitary type-satisfy Tutte-like equations, this allows us to show that in the perturbative regime they describe the different orders of the asymptotic topological expansion. Furthermore, they generalize the monotone Hurwitz numbers.
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