Pure and Applied Mathematics Seminar
Date/Time/Room: Thursday (4/26/2001) at 2:00pm in 487 PKH
Nicholas M. Ercolani,
Department of Mathematics,
University of Arizona
``Asymptotics and Integrable Structures for Biorthogonal Polynomials Associated to a Random Two-Matrix Model''Abstract: Recently the classical theory of orthogonal polynomials has been seen to play a central role in current developments within several areas of mathematics including random matrix theory, integrable systems theory, approximation theory and combinatorics. In this talk we describe a generalization of this classical theory to families of biorthogonal polynomials defined with respect to a planar measure. The class we consider plays a fundamental role in the analysis of certain random multi-matrix models. Also under deformations of the measure the recursion matrices for these polynomials evolve according to a semi-infinite generalization of the completely integrable full Kostant-Toda lattice. This connection could be relevant for understanding aspects of scaling limits for the multi-matrix model.