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arXiv · 2012.13829

Hahn polynomials and the Burnside process

Persi Diaconis·Chenyang Zhong
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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.

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Persi Diaconis, Chenyang Zhong. 2021-05-20. Hahn polynomials and the Burnside process. https://doi.org/10.1007/s11139-021-00482-z

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