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arxiv: 1107.1015 · v4 · pith:55XGLLHQnew · submitted 2011-07-06 · 🧮 math.CO · math-ph· math.AG· math.MP

Monotone Hurwitz numbers and the HCIZ integral

classification 🧮 math.CO math-phmath.AGmath.MP
keywords hcizintegralapproacharticleclassicalcoefficientscombinatorialcomplex
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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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