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Second order asymptotics for matrix models

Alice Guionnet·Edouard Maurel-Segala
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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.

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Alice Guionnet, Edouard Maurel-Segala. 2006-01-03. Second order asymptotics for matrix models. https://doi.org/10.1214/009117907000000141

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