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 |
|---|---|
| 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 |
