Second order asymptotics for matrix models
Probability
2011-11-09 v3
Abstract
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.
Cite
@article{arxiv.math/0601040,
title = {Second order asymptotics for matrix models},
author = {Alice Guionnet and Edouard Maurel-Segala},
journal= {arXiv preprint arXiv:math/0601040},
year = {2011}
}
Comments
Published in at http://dx.doi.org/10.1214/009117907000000141 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)