Lectures on random matrix models. The Riemann-Hilbert approach

Details Lectures on random matrix models. The Riemann-Hilbert approach Lectures on random matrix models. The Riemann-Hilbert approach

2008-01-11

arxiv.org/abs/0801.1858v2

Physics

Mathematical Physics

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

Scientific paper

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.

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