Topological expansion of unitary integrals and maps

  • Thomas Buc-d’Alché

    CNRS, Lyon, France
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Abstract

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. 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.

Cite this article

Thomas Buc-d’Alché, Topological expansion of unitary integrals and maps. Ann. Inst. Henri Poincaré Comb. Phys. Interact. (2024), published online first

DOI 10.4171/AIHPD/201