The Annals of Probability
- Ann. Probab.
- Volume 35, Number 6 (2007), 2160-2212.
Second order asymptotics for matrix models
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.
Ann. Probab., Volume 35, Number 6 (2007), 2160-2212.
First available in Project Euclid: 8 October 2007
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Guionnet, Alice; Maurel-Segala, Edouard. Second order asymptotics for matrix models. Ann. Probab. 35 (2007), no. 6, 2160--2212. doi:10.1214/009117907000000141. https://projecteuclid.org/euclid.aop/1191860419