The Poincaré inequality for Markov random fields proved via disagreement percolation

Jean René Chazottes; Frank Redig; Florian Völlering

doi:10.1016/j.indag.2011.09.003

The Poincaré inequality for Markov random fields proved via disagreement percolation

Jean René Chazottes
, Frank Redig
, Florian Völlering

Research output: Contribution to journal › Article › peer-review

Abstract

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 are able to prove the Poincaré inequality. For the whole subcritical regime, we have a weak Poincaré inequality and corresponding polynomial upper bound for the relaxation of the associated Glauber dynamics.

Original language	English
Pages (from-to)	149-164
Number of pages	16
Journal	Indagationes Mathematicae
Volume	22
Issue number	3-4
DOIs	https://doi.org/10.1016/j.indag.2011.09.003
Publication status	Published - 1 Jan 2011

Keywords

Coupling
Gibbs measures
Glauber dynamics
Poincaré inequality
Weak Poincaré inequality

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10.1016/j.indag.2011.09.003

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abstract = "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 are able to prove the Poincar{\'e} inequality. For 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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AU - Redig, Frank

AU - Völlering, Florian

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N2 - 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 are able to prove the Poincaré inequality. For the whole subcritical regime, we have a weak Poincaré inequality and corresponding polynomial upper bound for the relaxation of the associated Glauber dynamics.

AB - 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 are able to prove the Poincaré inequality. For the whole subcritical regime, we have a weak Poincaré inequality and corresponding polynomial upper bound for the relaxation of the associated Glauber dynamics.

KW - Coupling

KW - Gibbs measures

KW - Glauber dynamics

KW - Poincaré inequality

KW - Weak Poincaré inequality

UR - https://www.scopus.com/pages/publications/81055124210

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M3 - Article

AN - SCOPUS:81055124210

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VL - 22

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EP - 164

JO - Indagationes Mathematicae

JF - Indagationes Mathematicae

IS - 3-4

ER -

The Poincaré inequality for Markov random fields proved via disagreement percolation

Abstract

Keywords

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