Transportation inequalities: From Poisson to Gibbs measures

Abstract

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.

Published in at http://dx.doi.org/10.3150/00-BEJ268 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

References in corpus (4)

• Transportation cost-information inequalities and applications to random dynamical systems and diffusions
• Measure concentration for Euclidean distance in the case of dependent random variables
• Poincaré and transportation inequalities for Gibbs measures under the Dobrushin uniqueness condition
• On fine properties of mixtures with respect to concentration of measure and Sobolev type inequalities

Cited by in corpus (1)

• Transport inequalities for random point measures