Visibility and intersection density for Boolean models in hyperbolic space
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915691882348544 |
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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 |