Combinatorial aspects of matrix models

Abstract

We show that under reasonably general assumptions, the first order asymptotics of the free energy of matrix models are generating functions for colored planar maps. This is based on the fact that solutions of the Schwinger-Dyson equations are, by nature, generating functions for enumerating planar maps, a remark which bypasses the use of Gaussian calculus.

35 pages, 3 figures; corrected typos, additional section

References in corpus (4)

• Character Expansion Methods for Matrix Models of Dually Weighted Graphs
• Some Properties of Large $N$ Two Dimensional Yang--Mills Theory
• Master loop equations, free energy and correlations for the chain of matrices
• The degree distribution in bipartite planar maps: applications to the Ising model

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