Second order asymptotics for matrix models

Details Second order asymptotics for matrix models Second order asymptotics for matrix models

2006-01-03

arxiv.org/abs/math/0601040v3

Annals of Probability 2007, Vol. 35, No. 6, 2160-2212

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/009117907000000141 the Annals of Probability (http://www.imstat.org/aop/) by the Ins

Scientific paper

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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