FROM DISCRETE SURFACES AND MATRIX MODELS TO TOPOLOGICAL RECURSIONS. ll
VIDEO lecture recorded at IST Lisbon on 15/10/2009
by Nicholas Orantin
Abstract: This lecture describes asymptotic expansions of matrix integrals using graphs. Random matrix models represent a wonderful tool in the enumeration of random discrete surfaces of given topology. These lectures will address three issues. I will first properly define the concept of formal matrix integral used to build generating functions of discrete surfaces. I will then show that the enumeration of all possible ways of removing one edge from such a surface gives a set of loop equations which can be solved by induction in terms of an algebraic curve characterizing the considered matrix model: the spectral curve.
For More Information: For more information contact Paul Norbury email: P.Norbury@ms.unimelb.edu.au