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 . 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 . 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.
Keywords: Matrix models, Hurwitz numbers, asymptotic analysis
Mots-clés : Modèles matriciels, nombres de Hurwitz, analyse asymptotique
I. P. Goulden 1; Mathieu Guay-Paquet 2; Jonathan Novak 3
@article{AMBP_2014__21_1_71_0, 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}, number = {1}, year = {2014}, doi = {10.5802/ambp.336}, mrnumber = {3248222}, zbl = {1296.05202}, language = {en}, url = {https://ambp.centre-mersenne.org/articles/10.5802/ambp.336/} }
TY - JOUR AU - I. P. Goulden AU - Mathieu Guay-Paquet AU - Jonathan Novak TI - Monotone Hurwitz Numbers and the HCIZ Integral JO - Annales mathématiques Blaise Pascal PY - 2014 SP - 71 EP - 89 VL - 21 IS - 1 PB - Annales mathématiques Blaise Pascal UR - https://ambp.centre-mersenne.org/articles/10.5802/ambp.336/ DO - 10.5802/ambp.336 LA - en ID - AMBP_2014__21_1_71_0 ER -
%0 Journal Article %A I. P. Goulden %A Mathieu Guay-Paquet %A Jonathan Novak %T Monotone Hurwitz Numbers and the HCIZ Integral %J Annales mathématiques Blaise Pascal %D 2014 %P 71-89 %V 21 %N 1 %I Annales mathématiques Blaise Pascal %U https://ambp.centre-mersenne.org/articles/10.5802/ambp.336/ %R 10.5802/ambp.336 %G en %F AMBP_2014__21_1_71_0
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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