Open Access
November 2007 Second order asymptotics for matrix models
Alice Guionnet, Edouard Maurel-Segala
Ann. Probab. 35(6): 2160-2212 (November 2007). DOI: 10.1214/009117907000000141


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.


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Alice Guionnet. Edouard Maurel-Segala. "Second order asymptotics for matrix models." Ann. Probab. 35 (6) 2160 - 2212, November 2007.


Published: November 2007
First available in Project Euclid: 8 October 2007

zbMATH: 1129.15020
MathSciNet: MR2353386
Digital Object Identifier: 10.1214/009117907000000141

Primary: 05C30 , 15A52

Keywords: Map enumeration , random matrices

Rights: Copyright © 2007 Institute of Mathematical Statistics

Vol.35 • No. 6 • November 2007
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