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Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach
Percy Deift, New York University-Courant Institute of Mathematical Sciences, NY
A co-publication of the AMS and Courant Institute of Mathematical Sciences at New York University.
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Courant Lecture Notes
2000; 261 pp; softcover
Volume: 3
Reprint/Revision History:
reprinted 2002
ISBN-10: 0-8218-2695-6
ISBN-13: 978-0-8218-2695-9
List Price: US$35
Member Price: US$28
Order Code: CLN/3
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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
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