Matrix Models in Statistical Mechanics and Quantum Field Theory, Recent Examples and Problems

Abstract

We briefly describe the possibility of studying some simple vertex models on planar random graphs and a special model, related to famous colouring problems, which seems to allow a complete analytic solution. Next the analysis done few years ago of models with rectangular random matrices will be recalled as the approach seems to provide a method for an accurate evaluation of planar Green’s functions in quantum field theory in any dimension of space-time. The approach of random rectangular matrices makes use of the vast knowledge on vector models developed in the past two decades.