Abstract
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.
Acknowledgments
We wish to thank Steffen Betsch for making several useful comments. We also thank the referees for their very careful reading and for making several helpful suggestions.
Citation
Günter Last. Moritz Otto. "Disagreement coupling of Gibbs processes with an application to Poisson approximation." Ann. Appl. Probab. 33 (5) 4091 - 4126, October 2023. https://doi.org/10.1214/22-AAP1916
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