num_pages: 261
description: 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 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.
language: English
title: Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach
titlecomplete: Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach (Courant Lecture Notes)
ratings_count: 1
publisher: American Mathematical Society