2006/01/31 by Alice Guionnet, Edouard Maurel-Segala · 29 citations
Mathematics · #Advanced Combinatorial Mathematics #Central limit theorem #Function (biology) #Gaussian #Generating function #Matrix (chemical analysis) #Order (exchange) #Planar #Random Matrices and Applications #Random matrix #Regular polygon #Stochastic processes and statistical mechanics #math.PR #msc:05C30 #msc:15A52
paper · pdf · doi:10.1214/009117907000000141
published in The Annals of Probability 35(6) (Institute of Mathematical Statistics) · 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)
openalex publication_date 2007/11/01 · arxiv created 2007/11/22 · arxiv updated 2011/11/09 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.