Structure and eigenvalues of heat-bath Markov chains
arXiv:1301.4055 · doi:10.1016/j.laa.2014.04.018
Abstract
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.
15 pages. Minor edits to address referee's comments