Orthogonal polynomials and random matrices: a Riemann-Hilbert approach

Percy Deift0821826956, 9780821826959

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 $n {rightarrow} {infty}$? The main ingredient in the proof is the steepest descent method for oscillatory Riemann-Hilbert problems.