Rapid mixing and Markov bases
Combinatorics
2016-08-23 v3 Statistics Theory
Statistics Theory
Abstract
The mixing behaviour of random walks on lattice points of polytopes using Markov bases is examined. It is shown that under a dilation of the underlying polytope, these random walks do not mix rapidly when a fixed Markov basis is used. We also show that this phenomenon does not disappear after adding more moves to the Markov basis. Avoiding rejections by sampling applicable moves does also not lead to an asymptotic improvement. As a way out, a method of how to adapt Markov bases in order to achieve the fastest mixing behaviour is introduced.
Keywords
Cite
@article{arxiv.1505.03018,
title = {Rapid mixing and Markov bases},
author = {Tobias Windisch},
journal= {arXiv preprint arXiv:1505.03018},
year = {2016}
}
Comments
19 pages, 2 figures, v3: improved version, final version as in SIAM Journal on Discrete Mathematics