English

Visibility and intersection density for Boolean models in hyperbolic space

Probability 2025-12-24 v2 Metric Geometry

Abstract

For Poisson particle processes in hyperbolic space we introduce and study concepts analogous to the intersection density and the mean visible volume, which were originally considered in the analysis of Boolean models in Euclidean space. In particular, we determine a necessary and sufficient condition for the finiteness of the mean visible volume of a Boolean model in terms of the intensity and the mean surface area of the typical grain.

Keywords

Cite

@article{arxiv.2501.13447,
  title  = {Visibility and intersection density for Boolean models in hyperbolic space},
  author = {Tillmann Bühler and Daniel Hug and Christoph Thaele},
  journal= {arXiv preprint arXiv:2501.13447},
  year   = {2025}
}
R2 v1 2026-06-28T21:14:29.903Z