An explicit Dobrushin uniqueness region for Gibbs point processes with repulsive interactions
Probability
2022-04-06 v4
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 and inverse temperature . 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.
Cite
@article{arxiv.2009.06352,
title = {An explicit Dobrushin uniqueness region for Gibbs point processes with repulsive interactions},
author = {Pierre Houdebert and Alexander Zass},
journal= {arXiv preprint arXiv:2009.06352},
year = {2022}
}
Comments
To appear in Journal of Applied Probability 59.2 (June 2022). 20 pages, 3 figures