Global asymptotics of the discrete Chebyshev polynomials

Abstract

In this paper, we study the asymptotics of the discrete Chebyshev polynomials t_n(z,N) as the degree grows to infinity. Global asymptotic formulas are obtained as n→∞, when the ratio of the parameters n/N=c is a constant in the interval (0,1). Our method is based on a modified version of the Riemann–Hilbert approach first introduced by Deift and Zhou.