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arXiv · 1903.00054

On a property of random walk polynomials involving Christoffel functions

Erik A. van Doorn·Ryszard Szwarc
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Abstract

Discrete-time birth-death processes may or may not have certain properties known as asymptotic aperiodicity and the strong ratio limit property. In all cases known to us a suitably normalized process having one property also possesses the other, suggesting equivalence of the two properties for a normalized process. We show that equivalence may be translated into a property involving Christoffel functions for a type of orthogonal polynomials known as random walk polynomials. The prevalence of this property - and thus the equivalence of asymptotic aperiodicity and the strong ratio limit property for a normalized birth-death process - is proven under mild regularity conditions.

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Erik A. van Doorn, Ryszard Szwarc. 2019-02-28. On a property of random walk polynomials involving Christoffel functions. https://doi.org/10.1016/j.jmaa.2019.04.012

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