Riemann--Hilbert Problems
Mathematical Physics
2019-03-21 v1 Dynamical Systems
math.MP
Abstract
These lectures introduce the method of nonlinear steepest descent for Riemann-Hilbert problems. This method finds use in studying asymptotics associated to a variety of special functions such as the Painlev\'{e} equations and orthogonal polynomials, in solving the inverse scattering problem for certain integrable systems, and in proving universality for certain classes of random matrix ensembles. These lectures highlight a few such applications.
Cite
@article{arxiv.1903.08304,
title = {Riemann--Hilbert Problems},
author = {Percy Deift},
journal= {arXiv preprint arXiv:1903.08304},
year = {2019}
}