Talk 4175 data/Spring

Integrable Systems Seminar
Thursday, April 4, 2002, 4:00pm, 114 Physics
Nicholas Ercolani (University of Arizona)
Asymptotics of the Partition Function for Random Matrices with Applications to Graphical Enumeration

This talk will describe some recent joint work with Ken McLaughlin in which we study the partition function in random matrix theory using a well-known connection to orthogonal polynomials, and recently developed Riemann-Hilbert approach to the computation of asymptotics for these orthogonal polynomials. We obtain a detailed large N expansion for the partition function, for a general class of probability measures on hermitian matrices. A particular application I will discuss concerns the problem of the enumeration of graphs with general valences on Riemann surfaces of arbitrary finite genus.

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