Monotone Hurwitz Numbers and the HCIZ Integral  [ Les nombres de Hurwitz monotones et l’intégrale HCIZ ]
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 : https://doi.org/10.5802/ambp.336
Classification : 05E10,  15B62,  14N10
Mots clés : Modèles matriciels, nombres de Hurwitz, analyse asymptotique
@article{AMBP_2014__21_1_71_0,
     author = {Goulden, I. P. and Guay-Paquet, Mathieu and Novak, Jonathan},
     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},
     number = {1},
     year = {2014},
     doi = {10.5802/ambp.336},
     mrnumber = {3248222},
     zbl = {1296.05202},
     language = {en},
     url = {www.numdam.org/item/AMBP_2014__21_1_71_0/}
}
Goulden, I. P.; Guay-Paquet, Mathieu; Novak, Jonathan. Monotone Hurwitz Numbers and the HCIZ Integral. Annales Mathématiques Blaise Pascal, Tome 21 (2014) no. 1, pp. 71-89. doi : 10.5802/ambp.336. http://www.numdam.org/item/AMBP_2014__21_1_71_0/

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