Monotone Hurwitz numbers and the HCIZ integral
  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. 
Ian P. Goulden, Mathieu Guay-Paquet, Jonathan Novak
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