An urn model for the Jacobi-Piñeiro polynomials

2021/05/03 by F. Alberto Grünbaum, Grünbaum, F. Alberto, Manuel D. de la Iglesia +1 · 1 citation
Mathematics · #15A23 #33C45 #42C05 #60J10 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Probability (math.PR) #math.CA #math.PR #msc:15A23 #msc:33C45 #msc:42C05 #msc:60J10

paper · pdf · doi:10.48550/arxiv.2105.00614

10 pages, 5 figures

arxiv created 2021/05/03 · arxiv updated 2021/05/04

Abstract

The list of physically motivated urn models that can be solved in terms of classical orthogonal polynomials is very small. It includes a model proposed by D. Bernoulli and further analyzed by S. Laplace and a model proposed by P. and T. Ehrenfest and eventually connected with the Krawtchouk and Hahn polynomials. This connection was reversed recently in the case of the Jacobi polynomials where a rather contrived, and later a simpler urn model was proposed. Here we consider an urn model going with the Jacobi-Piñeiro multiple orthogonal polynomials. These polynomials have recently been put forth in connection with a stochastic matrix.

Cited by

• A Rodrigues Formula for Multiple Orthogonal Polynomials on the Simplex

Related

• An urn model associated with the Jacobi polynomials
• The bilateral birth-death chain generated by the associated Jacobi polynomials
• Multiple Orthogonal Polynomials and Random Walks
• Hypergeometric Multiple Orthogonal Polynomials and Random Walks
• QBD processes associated with Jacobi-Koornwinder bivariate polynomials and urn models