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.
వర్గాలు:
సంవత్సరం:
2000
ప్రచురణకర్త:
American Mathematical Society
భాష:
english
పేజీల సంఖ్య:
269
ISBN 10:
0821826956
ISBN 13:
9780821826959
పుస్తక శ్రేణి:
Courant Lecture Notes
ఫైల్:
DJVU, 1.55 MB
IPFS:
,
english, 2000