Annales Mathématiques
Blaise Pascal
no. 1
Monotone Hurwitz Numbers and the HCIZ Integral
[Les nombres de Hurwitz monotones et l’intégrale HCIZ]
I. P. Goulden1 ; Mathieu Guay-Paquet2 ; Jonathan Novak3
1 Department of Combinatorics & Optimization University of Waterloo 200 University Avenue West Waterloo, ON N2L 3G1 Canada
2 LaCIM Université du Québec à Montréal 201 Avenue du Président-Kennedy Montréal, QC H2X 3Y7 Canada
3 Department of Mathematics Massachusetts Institute of Technology 77 Massachusetts Ave. Boston, MA 02114 USA
Annales mathématiques Blaise Pascal, Tome 21 (2014) no. 1, pp. 71-89.

Nous démontrons que la convergence de l’énergie libre de l’intégrale HCIZ dans le plan complexe est équivalente à la non-nullité de l’intégrale HCIZ autour de z=0. Notre approche est basée sur un modèle combinatoire pour les coefficients de Maclaurin de l’intégrale HCIZ et sur des méthodes classiques d’analyse complexe.

In this article, we prove that the complex convergence of the HCIZ free energy is equivalent to the non-vanishing of the HCIZ integral in a neighbourhood of z=0. Our approach is based on a combinatorial model for the Maclaurin coefficients of the HCIZ integral together with classical complex-analytic techniques.

DOI : 10.5802/ambp.336
Classification : 05E10, 15B62, 14N10
Keywords: Matrix models, Hurwitz numbers, asymptotic analysis
Mot clés : Modèles matriciels, nombres de Hurwitz, analyse asymptotique

I. P. Goulden 1 ; Mathieu Guay-Paquet 2 ; Jonathan Novak 3

1 Department of Combinatorics & Optimization University of Waterloo 200 University Avenue West Waterloo, ON N2L 3G1 Canada
2 LaCIM Université du Québec à Montréal 201 Avenue du Président-Kennedy Montréal, QC H2X 3Y7 Canada
3 Department of Mathematics Massachusetts Institute of Technology 77 Massachusetts Ave. Boston, MA 02114 USA 
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I. P. Goulden; Mathieu Guay-Paquet; Jonathan Novak. Monotone Hurwitz Numbers and the HCIZ Integral. Annales mathématiques Blaise Pascal, Tome 21 (2014) no. 1, pp. 71-89. doi : 10.5802/ambp.336. https://ambp.centre-mersenne.org/articles/10.5802/ambp.336/

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