Transportation inequalities: From Poisson to Gibbs measures

TL;DR

This paper develops optimal transportation inequalities for Poisson and Gibbs measures, providing sharp bounds under certain conditions, which enhance understanding of measure concentration in stochastic processes.

Contribution

It introduces new transportation inequalities for Poisson and Gibbs measures, extending existing results and establishing sharp bounds under the Dobrushin uniqueness condition.

Findings

Optimal transportation inequality for Poisson measure established.

Sharp transportation inequality for Gibbs measure under Dobrushin condition.

Results applicable to both discrete and continuum configuration spaces.

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.