An explicit continuum Dobrushin uniqueness criterion for Gibbs point processes with non-negative pair potentials

Autoren: Pierre Houdebert, Alexander Zass (2020)

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 z and inverse temperature β. 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.

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