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Pré-Publication, Document De Travail Année : 2023

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.
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Dates et versions

hal-04077542 , version 1 (21-04-2023)
hal-04077542 , version 2 (24-04-2023)

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Thomas Buc-d'Alché. Topological expansion of unitary integrals and maps. 2023. ⟨hal-04077542v2⟩

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