%0 Journal Article
%T A Probablistic Origin for a New Class of Bivariate Polynomials
%A Michael R. Hoare
%A Mizan Rahman
%J Mathematics
%D 2008
%I arXiv
%R 10.3842/SIGMA.2008.089
%X 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.
%U http://arxiv.org/abs/0812.3879v1