Disagreement percolation for marked Gibbs point processes

Christoph Hofer-Temmel, Pierre Houdebert

Published 2017-09-13Version 1

We generalise disagreement percolation to Gibbs point processes of balls with varying radii. This allows to establish the uniqueness of the Gibbs measure and exponential decay of correlations in the high temperature regime by comparison with a sub-critical Boolean model. Applications to the continuum random cluster model and the Quermass-interaction model are presented. At the core of our proof lies an explicit dependent thinning from a Poisson point process to a dominated Gibbs point process.