Lectures on random matrix models. The Riemann-Hilbert approach

Abstract

This is a review of the Riemann-Hilbert approach to the large $N$ asymptotics in random matrix models and its applications. We discuss the following topics: random matrix models and orthogonal polynomials, the Riemann-Hilbert approach to the large $N$ asymptotics of orthogonal polynomials and its applications to the problem of universality in random matrix models, the double scaling limits, the large $N$ asymptotics of the partition function, and random matrix models with external source.

84 pages, 23 figures, to appear in the CRM volume on "Random Matrices", Springer, 2008

References in corpus (1)

• The Pearcey Process

Cited by in corpus (1)

• Gaussian matrix model in an external field and non-intersecting Brownian motions