Uniform Asymptotics for Polynomials Orthogonal With Respect to a General Class of Discrete Weights and Universality Results for Associated Ensembles

TL;DR

This paper develops uniform asymptotic formulas for orthogonal polynomials with discrete weights and establishes universality results for related ensembles, advancing understanding of their asymptotic behavior.

Contribution

It introduces new uniform asymptotic techniques for discrete orthogonal polynomials and proves universality results for associated ensembles, extending prior continuous-weight analyses.

Findings

Derived uniform asymptotics for a broad class of discrete orthogonal polynomials

Established universality results for ensembles related to these polynomials

Extended asymptotic analysis techniques to discrete weight settings

Abstract

This is the full version of "Uniform Asymptotics for Polynomials Orthogonal With Respect to a General Class of Discrete Weights and Universality Results for Associated Ensembles: Announcement of Results" appearing on this server and also published in IMRN 2003, no. 15, pp. 821-858.