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Monotone Hurwitz Numbers and the HCIZ Integral

I. P. Goulden; Mathieu Guay-Paquet; Jonathan Novak — 2014

Annales mathématiques Blaise Pascal

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.

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