An explicit Dobrushin uniqueness region for Gibbs point processes with repulsive interactions
- 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.
Author details: | Pierre HoudebertORCiD, Alexander ZassORCiDGND |
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DOI: | https://doi.org/10.1017/jpr.2021.70 |
ISSN: | 0021-9002 |
ISSN: | 1475-6072 |
Title of parent work (English): | Journal of applied probability / Applied Probability Trust |
Publisher: | Cambridge Univ. Press |
Place of publishing: | Cambridge |
Publication type: | Article |
Language: | English |
Date of first publication: | 2022/03/30 |
Publication year: | 2022 |
Release date: | 2023/04/03 |
Tag: | DLR equations; Dobrushin criterion;; Gibbs point process; cluster expansion; disagreement percolation; uniqueness |
Volume: | 59 |
Issue: | 2 |
Number of pages: | 15 |
First page: | 541 |
Last Page: | 555 |
Funding institution: | Deutsche Forschungsgemeinschaft (DFG) [318763901 - SFB1294];; Deutsch-Franzosische Hochschule (DFH) [DFDK 01-18] |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
Peer review: | Referiert |