Work

Topological expansion of unitary integrals and maps

Year: 2024

Type: article

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.

Source: Annales de l’Institut Henri Poincaré D Combinatorics Physics and their Interactions

DOI: 10.4171/aihpd/201

Author: Thomas Buc-d’Alché

Institution: Centre National de la Recherche Scientifique

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4404245384

FWCI: 2.267

Cites:

Cited by: 2

Related to: 10