Transportation inequalities: From Poisson to Gibbs measures
  We establish an optimal transportation inequality for the Poisson measure on the configuration space. Furthermore, under the Dobrushin uniqueness condition, we obtain a sharp transportation inequality for the Gibbs measure on $\mathbb{N}^{\Lambda}$ or the continuum Gibbs measure on the configuration space. 
Yutao Ma, Shi Shen, Xinyu Wang, Liming Wu
math.ST stat.TH