Visibility and intersection density for Boolean models in hyperbolic space

Tillmann Bühler; Daniel Hug; Christoph Thaele

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arXiv · 2501.13447

Visibility and intersection density for Boolean models in hyperbolic space

Tillmann Bühler·Daniel Hug·Christoph Thaele

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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.

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Tillmann Bühler, Daniel Hug, Christoph Thaele. 2025-01-23. Visibility and intersection density for Boolean models in hyperbolic space. https://arxiv.org/abs/2501.13447

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