  We consider the large-$N$ asymptotics of a system of discrete orthogonal
polynomials on an infinite regular lattice of mesh $\frac{1}{N}$, with weight
$e^{-NV(x)}$, where $V(x)$ is a real analytic function with sufficient growth
at infinity. The proof is based on 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.
