High order expansion of matrix models and enumeration of maps

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.

arXiv comment35 pages, 3 figures

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• Duality, Biorthogonal Polynomials and Multi-Matrix Models
• The degree distribution in bipartite planar maps: applications to the Ising model
• Combinatorial aspects of matrix models
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Cited by in corpus (7)

• Asymptotics of unitary and othogonal matrix integrals
• Second order asymptotics for matrix models
• On the Complex Asymptotics of the HCIZ and BGW Integrals
• Genus expansion for real Wishart matrices
• Duality of real and quaternionic random matrices
• Topological expansion of unitary integrals and maps
• Asymptotic normality for traces of polynomials in independent complex Wishart matrices