### On the probabilistic origin of some classical orthogonal polynomials in one and two variables

Rahman, M *(Carleton)*

Tuesday 30 June 2009, 15:30-16:30

Seminar Room 1, Newton Institute

#### Abstract

We will give a brief review of the previous work by the author and his collaborators featuring a so-called " dynamic urn model" that gives rise to transition probability kernels whose eigenfunctions are some of the classical orthogonal polynomials, both discrete and continuous.A more recent investigation by essentially the same authors involves what we call "Cumulative Bernoulli Trials",leads to a kernel in two independent variables and four probability parameters. The eigenfunctions of this kernel have been shown to be the Krawtchouk polynomials in two variables. Connection of these polynomials with the 9-j symbols of Quantum Angular Momentum theory as well as their q-extensions will also be discussed.

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