Poincar\'e inequality for Markov random fields via disagreement percolation
Probability
2011-09-21 v3 Mathematical Physics
math.MP
Abstract
We consider Markov random fields of discrete spins on the lattice . We use a technique of coupling of conditional distributions. If under the coupling the disagreement cluster is "sufficiently" subcritical, then we prove the Poincar\'e inequality. In the whole subcritical regime, we have a weak Poincar\'e inequality and corresponding polynomial upper bound for the relaxation of the associated Glauber dynamics.
Keywords
Cite
@article{arxiv.1012.2489,
title = {Poincar\'e inequality for Markov random fields via disagreement percolation},
author = {J. -R. Chazottes and F. Redig and F. Völlering},
journal= {arXiv preprint arXiv:1012.2489},
year = {2011}
}
Comments
21 pages, a few corrections made. To appear in Indagationes Mathematicae (special issue in the memory of F. Takens)