Disagreement percolation for Gibbs ball models
- We generalise disagreement percolation to Gibbs point processes of balls with varying radii. This allows to establish the uniqueness of the Gibbs measure and exponential decay of pair correlations in the low activity regime by comparison with a sub-critical Boolean model. Applications to the Continuum Random Cluster model and the Quermass-interaction model are presented. At the core of our proof lies an explicit dependent thinning from a Poisson point process to a dominated Gibbs point process. (C) 2018 Elsevier B.V. All rights reserved.
| Author details: | Christoph Hofer-Temmel, Pierre HoudebertORCiD |
|---|---|
| DOI: | https://doi.org/10.1016/j.spa.2018.11.003 |
| ISSN: | 0304-4149 |
| ISSN: | 1879-209X |
| Title of parent work (English): | Stochastic processes and their application |
| Publisher: | Elsevier |
| Place of publishing: | Amsterdam |
| Publication type: | Article |
| Language: | English |
| Date of first publication: | 2019/11/05 |
| Publication year: | 2018 |
| Release date: | 2020/11/04 |
| Tag: | Boolean model; Continuum random cluster model; Dependent thinning; Disagreement percolation; Exponential decay of pair correlation; Phase transition; Stochastic domination; Unique Gibbs state |
| Volume: | 129 |
| Issue: | 10 |
| Number of pages: | 19 |
| First page: | 3922 |
| Last Page: | 3940 |
| Funding institution: | Labex CEMPI [ANR-11-LAB X-0007-01]; Geometric stochastique [GDR 3477]; ANR "Percolation et percolation de premier passage"French National Research Agency (ANR) [ANR-16-CE40-0016] |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Peer review: | Referiert |
| Publishing method: | Open Access |
| Open Access / Green Open-Access |
