Poincar\'{e} and transportation inequalities for Gibbs measures under the Dobrushin uniqueness condition

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.Comment: Published 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