Monotone Hurwitz Numbers and the HCIZ Integral

I. P. Goulden; Mathieu Guay-Paquet; Jonathan Novak

doi:10.5802/ambp.336

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

Annales mathématiques Blaise Pascal, Volume 21 (2014) no. 1, pp. 71-89.

Abstract
Résumé

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.

MR: 3248222 | Zbl: 1296.05202

DOI: 10.5802/ambp.336

Classification: 05E10, 15B62, 14N10
Keywords: Matrix models, Hurwitz numbers, asymptotic analysis

Author's affiliations:

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

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     author = {I. P. Goulden and Mathieu Guay-Paquet and Jonathan Novak},
     title = {Monotone {Hurwitz} {Numbers} and the {HCIZ} {Integral}},
     journal = {Annales math\'ematiques Blaise Pascal},
     pages = {71--89},
     publisher = {Annales math\'ematiques Blaise Pascal},
     volume = {21},
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     year = {2014},
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     zbl = {1296.05202},
     language = {en},
     url = {https://ambp.centre-mersenne.org/articles/10.5802/ambp.336/}
}

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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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