A Probablistic Origin for a New Class of Bivariate Polynomials

We present here a probabilistic approach to the generation of new polynomials in two discrete variables. This extends our earlier work on the 'classical' orthogonal polynomials in a previously unexplored direction, resulting in the discovery of an exactly soluble eigenvalue problem corresp...

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Bibliographic Details
Main Authors: Michael R. Hoare, Mizan Rahman
Format: Article
Language:English
Published: National Academy of Science of Ukraine 2008-12-01
Series:Symmetry, Integrability and Geometry: Methods and Applications
Subjects:
Online Access:http://dx.doi.org/10.3842/SIGMA.2008.089
Description
Summary:We present here a probabilistic approach to the generation of new polynomials in two discrete variables. This extends our earlier work on the 'classical' orthogonal polynomials in a previously unexplored direction, resulting in the discovery of an exactly soluble eigenvalue problem corresponding to a bivariate Markov chain with a transition kernel formed by a convolution of simple binomial and trinomial distributions. The solution of the relevant eigenfunction problem, giving the spectral resolution of the kernel, leads to what we believe to be a new class of orthogonal polynomials in two discrete variables. Possibilities for the extension of this approach are discussed.
ISSN:1815-0659