Coupling of Markov Processes and Holley’s Inequalities for Gibbs Measures Statistical Application of Gibbs Measures

The purpose of this paper is to generalize Holley’s inequalities in the case of an attractive potential U associated with a Gibbs measure μ defined on ℤd. The main idea is to consider U as a strongly supermodular potential. Next, using coupling techniques, we obtain new inequalities for the correlation function ρ of the Gibbs measure. Finally, we give a non-physical application of Gibbs measures by studying an epidemiological problem concerning the withering of oak trees in a French department.