arXiv:2108.06303 Abstract | arXiv Analytics

arXiv:2108.06303 [math.PR]Abstract References Reviews Resources

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

Published 2021-08-13Version 1

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.

Comments: 23 pages, 5 tables

Categories: math.PR

Subjects: 60K35, 60G55, 60D05

Keywords: subcritical pair potential, gibbs distributions, associated poisson-driven random connection model, gibbs process, uniqueness results

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