On the uniqueness of Gibbs distributions with a non-negative and subcritical pair potential

Abstract

We prove that the distribution of a Gibbs process with non-negative pair potential is uniquely determined as soon as an associated Poisson-driven random connection model (RCM) does not percolate. Our proof combines disagreement coupling in continuum with a coupling of a Gibbs process and a RCM. The improvement over previous uniqueness results is illustrated both in theory and simulations.

23 pages, 5 tables

References in corpus (3)

• Effect of Dimensionality on the Continuum Percolation of Overlapping Hyperspheres and Hypercubes: II. Simulation Results and Analyses
• The Continuum Potts Model at the Disorder-Order Transition -- a Study by Cluster Dynamics
• An explicit Dobrushin uniqueness region for Gibbs point processes with repulsive interactions

Cited by in corpus (2)

• Structural properties of Gibbsian point processes in abstract spaces
• Potential-weighted connective constants and uniqueness of Gibbs measures