Disagreement coupling of Gibbs processes with an application to Poisson approximation
Probability
2023-01-24 v4
Abstract
We discuss a thinning and an embedding procedure to construct finite Gibbs processes with a given Papangelou intensity. Extending the approach in Hofer-Temmel (2019) and Hofer-Temmel and Houdebert (2019) 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.
Keywords
Cite
@article{arxiv.2104.00737,
title = {Disagreement coupling of Gibbs processes with an application to Poisson approximation},
author = {Günter Last and Moritz Otto},
journal= {arXiv preprint arXiv:2104.00737},
year = {2023}
}
Comments
41 pages