Intersection density and visibility for Boolean models in hyperbolic space
Bühler, Tillmann; Hug, Daniel
1; Thaele, Christoph
1 Institut für Stochastik (STOCH), Karlsruher Institut für Technologie (KIT)
1; Thaele, Christoph1 Institut für Stochastik (STOCH), Karlsruher Institut für Technologie (KIT)
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.
| Zugehörige Institution(en) am KIT | Institut für Stochastik (STOCH) |
| Publikationstyp | Forschungsbericht/Preprint |
| Publikationsjahr | 2025 |
| Sprache | Englisch |
| Identifikator | KITopen-ID: 1000185264 |
| Verlag | arxiv |
| Umfang | 21 S. |
| Schlagwörter | Probability (math.PR), Metric Geometry (math.MG), 52A22, 52A55, 60D05 |
| Nachgewiesen in | OpenAlex arXiv Dimensions |