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

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...

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Bibliographic Details
Published in:arXiv.org 2021-08
Main Authors: Betsch, Steffen, Last, Günter
Format: Article
Language:English
Subjects:
Coupling
Uniqueness
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2108.06303