Disagreement percolation for marked Gibbs point processes

Christoph Hofer-Temmel , Pierre Houdebert (1)

1 LPP - Laboratoire Paul Painlevé - UMR 8524

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.

Mots clés: continuum random cluster model; Quermass-interaction model; Widom-Rowlinson model; disagreement percolation; dependent thinning; Boolean model; stochastic domination; phase transition; unique Gibbs state; exponential decay of correlations

Domaines: Mathématiques [math]

Christoph Hofer-Temmel, Pierre Houdebert. Disagreement percolation for marked Gibbs point processes. 2017. ⟨hal-01622119v1⟩