DISAGREEMENT COUPLING OF GIBBS PROCESSES WITH AN APPLICATION TO POISSON APPROXIMATION

• 成果类型: Article
• 署名作者: Last, Guenter; Otto, Moritz
• 署名单位: Helmholtz Association; Karlsruhe Institute of Technology; Aarhus University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/22-AAP1916
• 发表日期: 2023
• 页码: 4091-4126
• 关键词: point-processes; PHASE-TRANSITION; percolation; EXISTENCE; intensity

摘要

We discuss a thinning and an embedding procedure to construct finite Gibbs processes with a given Papangelou intensity. Extending the approach of Hofer-Temmel (Electron. J. Probab. 24 (2019) 1-22) and Hofer-Temmel and Houdebert (Stochastic Process. Appl. 129 (2019) 3922-3940) we will use this to couple two finite Gibbs processes with different boundary conditions. As one application we will establish Poisson approximation of point processes derived from certain infinite volume Gibbs processes via dependent thinning. As another application we shall discuss empty space probabilities of certain Gibbs processes.