Orthogonal polynomials and random matrices : a Riemann-Hilbert approach

By: Percy DeiftMaterial type: TextTextSeries: Courant Lecture Notes ; Vol. 3Publication details: Rhode Island: American Mathematical Society: [c1998]Description: 261 pISBN: 9780821826959LOC classification: QA 404.5
Contents:
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
Summary: 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×n matrices exhibit universal behavior as n→∞? The main ingredient in the proof is the steepest descent method for oscillatory Riemann-Hilbert problems. --- summary provided by publisher
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Book Book ICTS
Mathematic Rack No 6 QA 404.5 (Browse shelf (Opens below)) Available Invoice no. IN 1199 ; Date: 09-12-2019 02306
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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

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×n matrices exhibit universal behavior as n→∞? The main ingredient in the proof is the steepest descent method for oscillatory Riemann-Hilbert problems. --- summary provided by publisher

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