Topological expansion of unitary integrals and maps
Résumé
In 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 expan-
sion, established previously by Guionnet and Novak. The maps we introduce – the maps of
unitary type – satisfy Tutte-like equations. It 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.
Domaines
Probabilités [math.PR]
Origine : Fichiers produits par l'(les) auteur(s)