Hahn polynomials and the Burnside process
Probability
2022-07-20 v2 Classical Analysis and ODEs
Abstract
We study a natural Markov chain on 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.
Keywords
Cite
@article{arxiv.2012.13829,
title = {Hahn polynomials and the Burnside process},
author = {Persi Diaconis and Chenyang Zhong},
journal= {arXiv preprint arXiv:2012.13829},
year = {2022}
}
Comments
29 pages; added Section 6 on a continuous limit of the Burnside process; improved the range of the parameter in Theorem 5.2; minor edits