Uniform Asymptotics for Discrete Orthogonal Polynomials with Respect to Varying Exponential Weights on a Regular Infinite Lattice.

We consider the large N asymptotics of a system of discrete orthogonal polynomials on an infinite regular lattice of mesh N1/N, with weight e−NV (x), where V (x) is a real analytic function with sufficient growth at infinity. The proof is based on the formulation of an interpolation problem for discrete orthogonal polynomials, which can be converted to a Riemann–Hilbert problem, and steepest descent analysis of this Riemann–Hilbert problem. [ABSTRACT FROM PUBLISHER]