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 |
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URL: | https://math-mprf.org/journal/articles/id1643/ |
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 |