Poincaré inequality for Markov random fields via disagreement percolation

Details Poincaré inequality for Markov random fields via disagreement percolation Poincaré inequality for Markov random fields via disagreement percolation

2010-12-11

arxiv.org/abs/1012.2489v3

Mathematics

Probability

21 pages, a few corrections made. To appear in Indagationes Mathematicae (special issue in the memory of F. Takens)

Scientific paper

We consider Markov random fields of discrete spins on the lattice $\Zd$. 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.

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