An explicit Dobrushin uniqueness region for Gibbs point processes with repulsive interactions

Abstract

We present a uniqueness result for Gibbs point processes with interactions that come from a non-negative pair potential; in particular, we provide an explicit uniqueness region in terms of activity $z$ and inverse temperature $\beta$. The technique used relies on applying to the continuous setting the classical Dobrushin criterion. We also present a comparison to the two other uniqueness methods of cluster expansion and disagreement percolation, which can also be applied for this type of interactions.

arXiv commentTo appear in Journal of Applied Probability 59.2 (June 2022). 20 pages, 3 figures

References in corpus (7)

• Cluster expansion for abstract polymer models. New bounds from an old approach
• Abstract cluster expansion with applications to statistical mechanical systems
• The analyticity region of the hard sphere gas. Improved bounds
• Cluster expansions for Gibbs point processes
• Upper bounds for spatial point process approximations
• Marked Gibbs point processes with unbounded interaction: an existence result
• Phase transition for continuum Widom-Rowlinson model with random radii

Cited by in corpus (2)

• On the uniqueness of Gibbs distributions with a non-negative and subcritical pair potential
• Structural properties of Gibbsian point processes in abstract spaces