The Annals of Probability

Second order asymptotics for matrix models

Alice Guionnet and Edouard Maurel-Segala

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We study several-matrix models and show that when the potential is convex and a small perturbation of the Gaussian potential, the first order correction to the free energy can be expressed as a generating function for the enumeration of maps of genus one. In order to do that, we prove a central limit theorem for traces of words of the weakly interacting random matrices defined by these matrix models and show that the variance is a generating function for the number of planar maps with two vertices with prescribed colored edges.

Article information

Ann. Probab., Volume 35, Number 6 (2007), 2160-2212.

First available in Project Euclid: 8 October 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 15A52 05C30: Enumeration in graph theory

Random matrices map enumeration


Guionnet, Alice; Maurel-Segala, Edouard. Second order asymptotics for matrix models. Ann. Probab. 35 (2007), no. 6, 2160--2212. doi:10.1214/009117907000000141.

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