We prove that heat-bath chains (which we define in a general setting) have no negative eigenvalues. Two applications of this result are presented: one to single-site heat-bath chains for spin systems and one to a heat-bath Markov chain for sampling contingency tables. Some implications of our main result for the analysis of the mixing time of heat-bath Markov chains are discussed. We also prove an alternative characterisation of heat-bath chains, and consider possible generalisations.
Cite
@article{arxiv.1301.4055,
title = {Structure and eigenvalues of heat-bath Markov chains},
author = {Martin Dyer and Catherine Greenhill and Mario Ullrich},
journal= {arXiv preprint arXiv:1301.4055},
year = {2014}
}
Comments
15 pages. Minor edits to address referee's comments