Orthogonal polynomials and random matrices: a Riemann-Hilbert approach
Percy Deift
This volume expands on a set of lectures held at the Courant Institute on Riemann-Hilbert 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 Riemann-Hilbert problems.
Categories:
Year:
2000
Edition:
lectures
Publisher:
American Mathematical Society
Language:
english
Pages:
269
ISBN 10:
0821826956
ISBN 13:
9780821826959
Series:
NYU
File:
DJVU, 1.56 MB
IPFS:
,
english, 2000