English

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