Second order asymptotics for matrix models

By Alice Guionnet, Édouard Maurel-Segala. 2006

53 citations recorded by the source corpus.

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.

Subfields: Discrete Mathematics and Combinatorics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/45080ae17150b3ecd3a8706523df487cb7397a5c

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In Discrete Mathematics and Combinatorics

In Mathematical Physics

In Statistics and Probability

Citations in the corpus

Central Limit Theorems for Linear Statistics of Heavy Tailed Random Matrices (2013, background): “Finally, but this is not really our concern here, the ﬂuctuations of the trace of words in several random matrices were studied in [19, 29, 39, 30].”
Asymptotics of unitary and orthogonal matrix integrals (2006, background): “Such ‘topological’ expansions were shown also to hold in the large N limit, and then to match with the formal expansion on a mathematical level of rigor by two authors [16, 17, 23] and previously in the one matrix case in [1, 2] and [12].”