Random matrices and the Potts model on random graphs
Résumé
These are the lecture notes for a mini-course given in St. Petersburg School in Probability and Statistical Physics during June 18-29, 2012. The purpose of this course is to explain the uses of random matrices to compute the partition function of the Potts model taken on (certain) random planar maps. We start by explaining how matrix integrals can be used to enumerate maps, that is graphs which are sorted by the genus of the surface on which they can be properly embedded. We then see how this can be elaborated to enumerate loop models, and their relation with the Potts model on some random planar maps. Finally we use this relation to solve the combinatorial problem of computing generating functions of the Potts model.
Domaines
Probabilités [math.PR]
Origine : Fichiers produits par l'(les) auteur(s)
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