Asymptotics of orthogonal polynomials and the Painlevé transcendents

2016/08/16 by Dan Dai, Dai, Dan · 1 citation
Mathematics · #33E17 #34M55 #41A60 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Fractional Differential Equations Solutions #Iterative Methods for Nonlinear Equations #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.1608.04513

openalex publication_date 2016/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this survey, we review asymptotic results of some orthogonal polynomials which are relate to the Painlevé transcendents. They are obtained by applying Deift-Zhou's nonlinear steepest descent method for Riemann-Hilbert problems. In the last part of this article, we list several open problems.

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• The Instability of Painlevé Equations in Recovering Largest Eigenvalue Distributions of GUE, LUE, JUE and an Attempt of Solution to It

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