Orthogonal Polynomials and Random Matrices A Riemann-Hilbert Approach

This volume expands on a set of lectures held at the Courant Institute on Riemann-Hilbert problems, orthogonal polynomials, and random matrix theory. The goal of the course was to prove universality for a variety of statistical quantities arising in the theory of random matrix models. The central question was the following: Why do very general ensembles of random n times n matrices exhibit universal behavior as n > infinity? The main ingredient in the proof is the steepest descent method for oscillatory Riemann-Hilbert problems. Titles in this series are copublished with the Courant Institute of Mathematical Sciences at New York University.Deift, Percy is the author of 'Orthogonal Polynomials and Random Matrices A Riemann-Hilbert Approach' with ISBN 9780821826959 and ISBN 0821826956.