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.