Abstract
AbstractThe very classical Ehrenfest urn model can be solved exactly in terms of Krawtchouk polynomials. I consider a natural extension of this model which goes beyond “nearest neighbours” random walks and whose analysis benefits from the study of a family of matrix-valued orthogonal polynomials. This subject was started by M.G. Krein around 1949. This paper shows one more example of his vast and lasting legacy in the never-ending task of finding new mathematical tools to analyze the physical world.KeywordsMatrix-valued orthogonal polynomialsKarlin-McGregor representationKrawtchouk polynomialsMathematics Subject Classification (2000)33C45, 22E45
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