  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.
