Disagreement percolation for Gibbs ball models

Christoph Hofer-Temmel and Pierre Houdebert

Stochastic Processes and their Applications, 2019, vol. 129, issue 10, 3922-3940

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.

Keywords: Continuum random cluster model; Disagreement percolation; Dependent thinning; Boolean model; Stochastic domination; Phase transition; Unique Gibbs state; Exponential decay of pair correlation (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1016/j.spa.2018.11.003

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