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. 
Liming Wu