High order expansion of matrix models and enumeration of maps

Edouard Maurel-Segala

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arXiv · math/0608192

High order expansion of matrix models and enumeration of maps

Edouard Maurel-Segala

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Abstract

Perturbation of the GUE are known in physics to be related to enumeration of graphs on surfaces. We investigate this idea and show that for a small convex perturbation, we can perform a genus expansion: the moments of the empirical measure can be developed into a series whose g-th term is a generating function of graphs on a surface of genus g.

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Edouard Maurel-Segala. 2006-08-08. High order expansion of matrix models and enumeration of maps. https://arxiv.org/abs/math/0608192

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