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.

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