On the uniqueness of Gibbs distributions with a non-negative and subcritical pair potential
Probability
2023-09-29 v1
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.
Keywords
Cite
@article{arxiv.2108.06303,
title = {On the uniqueness of Gibbs distributions with a non-negative and subcritical pair potential},
author = {Steffen Betsch and Günter Last},
journal= {arXiv preprint arXiv:2108.06303},
year = {2023}
}
Comments
23 pages, 5 tables