Article contents
An explicit Dobrushin uniqueness region for Gibbs point processes with repulsive interactions
Published online by Cambridge University Press: 30 March 2022
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
MSC classification
- Type
- Original Article
- Information
- Copyright
- © The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust
References
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20220623172611105-0295:S002190022100070X:S002190022100070X_inline274.png?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20220623172611105-0295:S002190022100070X:S002190022100070X_inline275.png?pub-status=live)
- 3
- Cited by