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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Published in:arXiv.org 2021-08
Main Authors: Betsch, Steffen, Last, Günter
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Coupling
Uniqueness
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description 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.
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title On the uniqueness of Gibbs distributions with a non-negative and subcritical pair potential
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