Ideal Poisson-Voronoi tessellations on hyperbolic spaces
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866913886161076224 |
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| author | D'Achille, Matteo Curien, Nicolas Enriquez, Nathanaël Lyons, Russell Ünel, Meltem |
| author_facet | D'Achille, Matteo Curien, Nicolas Enriquez, Nathanaël Lyons, Russell Ünel, Meltem |
| contents | We study the limit in low intensity of Poisson--Voronoi tessellations in hyperbolic spaces $ \mathbb{H}_{d}$ for $d \geq 2$. In contrast to the Euclidean setting, a limiting nontrivial ideal tessellation $ \mathcal{V}_{d}$ appears as the intensity tends to $0$. The tessellation $ \mathcal{V}_{d}$ is a natural, isometry-invariant decomposition of $ \mathbb{H}_{d}$ into countably many unbounded polytopes, each with a unique end. We study its basic properties, in particular, the geometric features of its cells. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2303_16831 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Ideal Poisson-Voronoi tessellations on hyperbolic spaces D'Achille, Matteo Curien, Nicolas Enriquez, Nathanaël Lyons, Russell Ünel, Meltem Probability 60G55, 60D05 We study the limit in low intensity of Poisson--Voronoi tessellations in hyperbolic spaces $ \mathbb{H}_{d}$ for $d \geq 2$. In contrast to the Euclidean setting, a limiting nontrivial ideal tessellation $ \mathcal{V}_{d}$ appears as the intensity tends to $0$. The tessellation $ \mathcal{V}_{d}$ is a natural, isometry-invariant decomposition of $ \mathbb{H}_{d}$ into countably many unbounded polytopes, each with a unique end. We study its basic properties, in particular, the geometric features of its cells. |
| title | Ideal Poisson-Voronoi tessellations on hyperbolic spaces |
| topic | Probability 60G55, 60D05 |
| url | https://arxiv.org/abs/2303.16831 |