Gibbs point processes on path space
- We present general existence and uniqueness results for marked models with pair interactions, exemplified through Gibbs point processes on path space. More precisely, we study a class of infinite-dimensional diffusions under Gibbsian interactions, in the context of marked point configurations: the starting points belong to R-d, and the marks are the paths of Langevin diffusions. We use the entropy method to prove existence of an infinite-volume Gibbs point process and use cluster expansion tools to provide an explicit activity domain in which uniqueness holds.
| Author details: | Alexander ZassORCiDGND |
|---|---|
| DOI: | https://doi.org/10.20347/WIAS.PREPRINT.2859 |
| ISSN: | 1024-2953 |
| Title of parent work (English): | Markov processes and related fields |
| Subtitle (English): | existence, cluster expansion and uniqueness |
| Publisher: | Polymat |
| Place of publishing: | Moscow |
| Publication type: | Article |
| Language: | English |
| Date of first publication: | 2021/07/16 |
| Publication year: | 2021 |
| Release date: | 2024/07/29 |
| Tag: | DLR equations; cluster; expansion; infinite-dimensional diffusions; marked Gibbs point processes; uniqueness |
| Volume: | 28 |
| Issue: | 3 |
| Number of pages: | 36 |
| First page: | 329 |
| Last Page: | 364 |
| Funding institution: | Deutsche Forschungsgemeinschaft (DFG) [SFB1294/1 -318763901];; Deutsch-Französische 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 |
| License (German): |  Keine öffentliche Lizenz: Unter Urheberrechtsschutz |
