A Probablistic Origin for a New Class of Bivariate Polynomials

Autor:	Hoare, Michael R., Rahman, Mizan
Rok vydání:	2008
Předmět:	Mathematics - Classical Analysis and ODEs Mathematics - Probability
Zdroj:	SIGMA 4 (2008), 089, 18 pages
Druh dokumentu:	Working Paper
DOI:	10.3842/SIGMA.2008.089
Popis:	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. Comment: 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/
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/0812.3879 Zobrazit plný text záznamu View this record from Arxiv