**Courant Lecture Notes**

Volume: 3;
2000;
261 pp;
Softcover

MSC: Primary 30; 33; 60; 15; 26;

Print ISBN: 978-0-8218-2695-9

Product Code: CLN/3

List Price: $37.00

Individual Member Price: $29.60

**Electronic ISBN: 978-1-4704-3107-5
Product Code: CLN/3.E**

List Price: $37.00

Individual Member Price: $29.60

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# Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach

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*Percy Deift*

A co-publication of the AMS and the Courant Institute of Mathematical Sciences at New York University

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.

#### Table of Contents

# Table of Contents

## Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach

- Cover Cover11
- General editor information ii3
- Title page iii4
- Dedication v6
- Contents vii8
- Preface ix10
- Riemann-Hilbert problems 112
- Jacobi operators 1324
- Orthogonal polynomials 3748
- Continued fractions 5768
- Random matrix theory 89100
- Equilibrium measures 129140
- Asymptotics for orthogonal polynomials 181192
- Universality 237248
- Bibliography 259270
- Back Cover Back Cover1273

#### Readership

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