High order expansion of matrix models and enumeration of maps

Details High order expansion of matrix models and enumeration of maps High order expansion of matrix models and enumeration of maps

2006-08-08

arxiv.org/abs/math/0608192v1

Mathematics

Probability

35 pages, 3 figures

Scientific paper

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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