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Disagreement percolation for Gibbs ball models. (English) Zbl 1426.82016
Summary: 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.

##### MSC:
 82B21 Continuum models (systems of particles, etc.) arising in equilibrium statistical mechanics 60E15 Inequalities; stochastic orderings 60K35 Interacting random processes; statistical mechanics type models; percolation theory 60G55 Point processes (e.g., Poisson, Cox, Hawkes processes) 82B43 Percolation 60D05 Geometric probability and stochastic geometry 82B26 Phase transitions (general) in equilibrium statistical mechanics
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