Speaker: Alice Guionnet (ENS Lyon)
Title: Matrix models, the enumeration of maps and free probability
Abstract: I will discuss the asymptotics of multimatrix models. In a small parameters (or high temperature) region, their free energy is well known to converge and to be related with the enumeration of maps. The latter can be proved by relating the so-called Dyson-Schwinger equations with Tutte surgery by nice pictures. In general, the convergence of the free energy is unknown, a problem which is closely related with the lack of a full entropy theory in free probability. We will discuss few models that can be analyzed, in particular in the large parameters (or low temperature) region.