Hahn polynomials and the Burnside process

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 augm...

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Bibliographic Details
Published in:arXiv.org 2021-05
Main Authors: Diaconis, Persi, Zhong, Chenyang
Format: Article
Language:English
Subjects:
Algorithms
Binomial distribution
Eigenvectors
Markov chains
Permutations
Polynomials
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2012.13829