A probabilistic origin for a new class of bivariate polynomials
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Publication:1018714
DOI10.3842/SIGMA.2008.089zbMATH Open1163.33308arXiv0812.3879OpenAlexW2112743662MaRDI QIDQ1018714
Author name not available (Why is that?)
Publication date: 21 May 2009
Published in: (Search for Journal in Brave)
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.
Full work available at URL: https://arxiv.org/abs/0812.3879
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