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Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach

Percy Deift New York University-Courant Institute of Mathematical Sciences, New York, NY
A co-publication of the AMS and Courant Institute of Mathematical Sciences at New York University
Available Formats:
Softcover ISBN: 978-0-8218-2695-9
Product Code: CLN/3
List Price: $40.00 MAA Member Price:$36.00
AMS Member Price: $32.00 Electronic ISBN: 978-1-4704-3107-5 Product Code: CLN/3.E List Price:$37.00
MAA Member Price: $33.30 AMS Member Price:$29.60
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List Price: $60.00 MAA Member Price:$54.00
AMS Member Price: $48.00 Click above image for expanded view Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach Percy Deift New York University-Courant Institute of Mathematical Sciences, New York, NY A co-publication of the AMS and Courant Institute of Mathematical Sciences at New York University Available Formats:  Softcover ISBN: 978-0-8218-2695-9 Product Code: CLN/3  List Price:$40.00 MAA Member Price: $36.00 AMS Member Price:$32.00
 Electronic ISBN: 978-1-4704-3107-5 Product Code: CLN/3.E
 List Price: $37.00 MAA Member Price:$33.30 AMS Member Price: $29.60 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$60.00 MAA Member Price: $54.00 AMS Member Price:$48.00
• Book Details

Courant Lecture Notes
Volume: 32000; 261 pp
MSC: Primary 30; 33; 60; 15; 26;

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.

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

• Chapters
• Chapter 1. Riemann-Hilbert problems
• Chapter 2. Jacobi operators
• Chapter 3. Orthogonal polynomials
• Chapter 4. Continued fractions
• Chapter 5. Random matrix theory
• Chapter 6. Equilibrium measures
• Chapter 7. Asymptotics for orthogonal polynomials
• Chapter 8. Universality
• Requests

Review Copy – for reviewers who would like to review an AMS book
Accessibility – to request an alternate format of an AMS title
Volume: 32000; 261 pp
MSC: Primary 30; 33; 60; 15; 26;

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.

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

• Chapters
• Chapter 1. Riemann-Hilbert problems
• Chapter 2. Jacobi operators
• Chapter 3. Orthogonal polynomials
• Chapter 4. Continued fractions
• Chapter 5. Random matrix theory
• Chapter 6. Equilibrium measures
• Chapter 7. Asymptotics for orthogonal polynomials
• Chapter 8. Universality
Review Copy – for reviewers who would like to review an AMS book
Accessibility – to request an alternate format of an AMS title
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