%0 Journal Article
%T Second order asymptotics for matrix models
%A Alice Guionnet
%A Edouard Maurel-Segala
%J Mathematics
%D 2006
%I arXiv
%R 10.1214/009117907000000141
%X 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.
%U http://arxiv.org/abs/math/0601040v3