Monotone Hurwitz Numbers and the HCIZ Integral
Annales mathématiques Blaise Pascal, Volume 21 (2014) no. 1, pp. 71-89.

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.

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.

DOI: 10.5802/ambp.336
Classification: 05E10,  15B62,  14N10
Keywords: Matrix models, Hurwitz numbers, asymptotic analysis
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, Volume 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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