Riemann--Hilbert Problems (1903.08304v1)

Published 20 Mar 2019 in math-ph, math.DS, and 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.

Summary

We haven't generated a summary for this paper yet.

Whiteboard

Generate a whiteboard explanation of this paper.

Sign Up to Generate

Paper Prompts

Sign up for free to create and run prompts on this paper using GPT-5.

Top Community Prompts

Explain it Like I'm 14

Practical Applications

Conceptual Simplification

Sign Up to Activate View All Prompts

Open Problems

We haven't generated a list of open problems mentioned in this paper yet.

Continue Learning

We haven't generated follow-up questions for this paper yet.

Authors (1)

Percy Deift

Collections

Sign up for free to add this paper to one or more collections.