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This volume expands on a set of lectures held at the Courant Institute on RiemannHilbert 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 following: 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 RiemannHilbert problems.
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