Topological expansion of unitary integrals and maps

Fuente: arXiv
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Autore principale: Buc-d'Alché, Thomas
Natura: Preprint
Pubblicazione: 2023
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author Buc-d'Alché, Thomas
author_facet Buc-d'Alché, Thomas
contents 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 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.
format Preprint
id arxiv_https___arxiv_org_abs_2304_12785
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Topological expansion of unitary integrals and maps
Buc-d'Alché, Thomas
Probability
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 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.
title Topological expansion of unitary integrals and maps
topic Probability
url https://arxiv.org/abs/2304.12785