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.

Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.

Readership

Graduate students and research mathematicians interested in functions of a complex variable.

Table of Contents

• Riemann-Hilbert problems
• Jacobi operators
• Orthogonal polynomials
• Continued fractions
• Random matrix theory
• Equilibrium measures
• Asymptotics for orthogonal polynomials
• Universality
• Bibliography