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

TL;DR

This paper proves the uniqueness of Gibbs process distributions with non-negative pair potentials when the related random connection model does not percolate, using a novel coupling approach.

Contribution

It introduces a new proof method combining disagreement coupling and RCM coupling to establish uniqueness under subcritical conditions.

Findings

Uniqueness holds when the associated RCM does not percolate.

The proof improves upon previous results in theory and simulations.

Provides a new coupling-based approach for Gibbs process analysis.

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.