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arXiv · 1301.4055

Structure and eigenvalues of heat-bath Markov chains

Martin Dyer·Catherine Greenhill·Mario Ullrich
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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.

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Martin Dyer, Catherine Greenhill, Mario Ullrich. 2014-04-10. Structure and eigenvalues of heat-bath Markov chains. https://doi.org/10.1016/j.laa.2014.04.018

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