Heat-bath random walks with Markov bases
Combinatorics
2016-05-27 v1 Statistics Theory
Statistics Theory
Abstract
Graphs on lattice points are studied whose edges come from a finite set of allowed moves of arbitrary length. We show that the diameter of these graphs on fibers of a fixed integer matrix can be bounded from above by a constant. We then study the mixing behaviour of heat-bath random walks on these graphs. We also state explicit conditions on the set of moves so that the heat-bath random walk, a generalization of the Glauber dynamics, is an expander in fixed dimension.
Cite
@article{arxiv.1605.08386,
title = {Heat-bath random walks with Markov bases},
author = {Caprice Stanley and Tobias Windisch},
journal= {arXiv preprint arXiv:1605.08386},
year = {2016}
}
Comments
20 pages, 3 figures