Topological expansion for random matrices

Alice Guionnet, ENS, Lyon, France
Sherrerd Hall 101

It is known till 't Hooft and Brezin-Itzykson-Paris and Zuber that the partition function of random matrices expand formally as a generating function for the enumeration of graphs sorted by their genera. We shall show that this expansion can be turned into an asymptotic expansion in a wide variety of models, including the so-called beta models.