An urn model for the Jacobi-Pi\~neiro polynomials

TL;DR

This paper introduces an urn model linked to Jacobi-Pi eiro polynomials, expanding the class of physically motivated urn models solvable via classical orthogonal polynomials.

Contribution

It presents a new urn model associated with Jacobi-Pi eiro multiple orthogonal polynomials, connecting them to stochastic matrices.

Findings

Established a new urn model for Jacobi-Pi eiro polynomials

Connected the urn model with a stochastic matrix

Extended classical orthogonal polynomial urn models

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-Pi\~neiro multiple orthogonal polynomials. These polynomials have recently been put forth in connection with a stochastic matrix.