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Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach

Percy Deift, "Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach"
2000 | pages: 269 | ISBN: 0821826956 | DJVU | 1,6 mb

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.
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Tags: Orthogonal, Polynomials, Random, Matrices, Riemann, Approach

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