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

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

2006-11-21

arxiv.org/abs/math/0611635v1

Annals of Probability 2006, Vol. 34, No. 5, 1960-1989

Mathematics

Probability

Published at http://dx.doi.org/10.1214/009117906000000368 in the Annals of Probability (http://www.imstat.org/aop/) by the Ins

Scientific paper

10.1214/009117906000000368

In in this paper we establish an explicit and sharp estimate of the spectral
gap (Poincar\'{e} 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.

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