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# Orthogonal Polynomials and Random Matrices

A Riemann-Hilbert Approach

261 pages, parution le 01/10/2000

## Résumé

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 copublished with the Courant Institute of Mathematical Sciences at New York University.

Contents

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

## Caractéristiques techniques

 PAPIER Éditeur(s) American Mathematical Society (AMS) Auteur(s) Percy Deift Parution 01/10/2000 Nb. de pages 261 Format 18 x 25,3 Couverture Broché Poids 472g Intérieur Noir et Blanc EAN13 9780821826959 ISBN13 978-0-8218-2695-9

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