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

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

2009-09-10

arxiv.org/abs/0909.1985v3

Physics

Mathematical Physics

32 pages, 4 figures; corrected version

Scientific paper

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.

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