@article{HoferTemmelHoudebert2018, author = {Hofer-Temmel, Christoph and Houdebert, Pierre}, title = {Disagreement percolation for Gibbs ball models}, series = {Stochastic processes and their application}, volume = {129}, journal = {Stochastic processes and their application}, number = {10}, publisher = {Elsevier}, address = {Amsterdam}, issn = {0304-4149}, doi = {10.1016/j.spa.2018.11.003}, pages = {3922 -- 3940}, year = {2018}, abstract = {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 pair correlations in the low activity 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. (C) 2018 Elsevier B.V. All rights reserved.}, language = {en} }