Combinatorial aspects of matrix models

Details Combinatorial aspects of matrix models Combinatorial aspects of matrix models

2005-03-03

arxiv.org/abs/math/0503064v2

Mathematics

Probability

35 pages, 3 figures; corrected typos, additional section

Scientific paper

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.

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