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Recurrences for generating polynomials

Banff International Research Station for Mathematical Innovation and Discovery

In this talk we consider sequences of polynomials that satisfy differential--difference recurrences. Our interest is motivated by the fact that polynomials satisfying such recurrences frequently appear as generating polynomials of integer valued random variables that are of interest in discrete mathematics. It is, therefore, of interest to understand the properties of such polynomials and their probabilistic consequences. We will be primarily interested in the limiting distribution of the corresponding random variables and we give a few examples, leading to a Poisson, normal, and Rayleigh distributions.

Mathematics; Probability theory and stochastic processes; Statistics; Probability / statistical mechanics

video/mp4

Author affiliation: Drexel University

2017-11-27

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/63745

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/