Visibility and intersection density for Boolean models in hyperbolic space

Fuente: arXiv
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Main Authors: Bühler, Tillmann, Hug, Daniel, Thaele, Christoph
Format: Preprint
Published: 2025
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author Bühler, Tillmann
Hug, Daniel
Thaele, Christoph
author_facet Bühler, Tillmann
Hug, Daniel
Thaele, Christoph
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2501_13447
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Visibility and intersection density for Boolean models in hyperbolic space
Bühler, Tillmann
Hug, Daniel
Thaele, Christoph
Probability
Metric Geometry
52A22, 52A55, 60D05
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.
title Visibility and intersection density for Boolean models in hyperbolic space
topic Probability
Metric Geometry
52A22, 52A55, 60D05
url https://arxiv.org/abs/2501.13447