A Probablistic Origin for a New Class of Bivariate Polynomials
Abstract
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.
Cite
@article{arxiv.0812.3879,
title = {A Probablistic Origin for a New Class of Bivariate Polynomials},
author = {Michael R. Hoare and Mizan Rahman},
journal= {arXiv preprint arXiv:0812.3879},
year = {2008}
}
Comments
This is a contribution to the Special Issue on Dunkl Operators and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/