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An explicit Dobrushin uniqueness region for Gibbs point processes with repulsive interactions

Part of: Special processes

Published online by Cambridge University Press:  30 March 2022

Pierre Houdebert  and
Alexander Zass Open the ORCID record for Alexander Zass [Opens in a new window]
Pierre Houdebert*
Affiliation:
Universität Potsdam
Alexander Zass*
Affiliation:
Universität Potsdam, WIAS Berlin
*
*Postal address: Karl-Liebknecht Str. 24-25, 14476 Potsdam, Germany. Email: pierre.houdebert@gmail.com
**Postal address: Mohrenstr. 39, 10117 Berlin, Germany. Email: alexander.zass@wias-berlin.de
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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 z and inverse temperature $\beta$ . 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 interaction.

Keywords

Gibbs point processDLR equationsuniquenessDobrushin criterioncluster expansiondisagreement percolation

MSC classification

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Type
Original Article
Information
Journal of Applied Probability , Volume 59 , Issue 2 , June 2022 , pp. 541 - 555
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust

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