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Book DetailsCourant Lecture NotesVolume: 3; 2000; 261 ppMSC: 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.
Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.
ReadershipGraduate students and research mathematicians interested in functions of a complex variable.
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Table of Contents
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Chapters
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Chapter 1. Riemann-Hilbert problems
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Chapter 2. Jacobi operators
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Chapter 3. Orthogonal polynomials
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Chapter 4. Continued fractions
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Chapter 5. Random matrix theory
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Chapter 6. Equilibrium measures
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Chapter 7. Asymptotics for orthogonal polynomials
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Chapter 8. Universality
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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.
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
