Lectures on random matrix models. The Riemann-Hilbert approach

TL;DR

This paper reviews the Riemann-Hilbert method for analyzing large N asymptotics in random matrix models, covering orthogonal polynomials, universality, double scaling limits, and external sources.

Contribution

It provides a comprehensive overview of the Riemann-Hilbert approach and its applications to various problems in random matrix theory.

Findings

Riemann-Hilbert approach effectively analyzes large N asymptotics

Universal behavior in random matrix models is characterized

Partition function asymptotics are elucidated

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.