Poincaré and transportation inequalities for Gibbs measures under the Dobrushin uniqueness condition

Abstract

In in this paper we establish an explicit and sharp estimate of the spectral gap (Poincaré inequality) and the transportation inequality for Gibbs measures, under the Dobrushin uniqueness condition. Moreover, we give a generalization of the Liggett's $M-\epsilon$ theorem for interacting particle systems.

arXiv commentPublished at http://dx.doi.org/10.1214/009117906000000368 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (3)

• Transportation cost-information inequalities and applications to random dynamical systems and diffusions
• Absence of Phase Transition for Antiferromagnetic Potts Models via the Dobrushin Uniqueness Theorem
• Measure concentration for Euclidean distance in the case of dependent random variables

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