Hahn polynomials and the Burnside process

Abstract

We study a natural Markov chain on $\{0,1,\cdots ,n\}$ with eigenvectors the Hahn polynomials. This explicit diagonalization makes it possible to get sharp rates of convergence to stationarity. The process, the Burnside process, is a special case of the celebrated `Swendsen-Wang' or `data augmentation' algorithm. The description involves the beta-binomial distribution and Mallows model on permutations. It introduces a useful generalization of the Burnside process.

arXiv comment29 pages; added Section 6 on a continuous limit of the Burnside process; improved the range of the parameter in Theorem 5.2; minor edits

References in corpus (4)

• Askey--Wilson polynomials, quadratic harnesses and martingales
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• Tight Frame with Hahn and Krawtchouk Polynomials of Several Variables
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Cited by in corpus (3)

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