Softcover ISBN:  9780821826959 
Product Code:  CLN/3 
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Electronic ISBN:  9781470431075 
Product Code:  CLN/3.E 
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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 RiemannHilbert 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 RiemannHilbert problems.
ReadershipGraduate students and research mathematicians interested in functions of a complex variable.

Table of Contents

Chapters

Chapter 1. RiemannHilbert 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


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This volume expands on a set of lectures held at the Courant Institute on RiemannHilbert 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 RiemannHilbert problems.
Graduate students and research mathematicians interested in functions of a complex variable.

Chapters

Chapter 1. RiemannHilbert 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