Sharp asymptotics for the maximal distance from the boundary to the nucleus of a typical Poisson-Voronoi cell
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908653148176384 |
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| author | Calka, Pierre d'Errico, Cecilia Enriquez, Nathanaël |
| author_facet | Calka, Pierre d'Errico, Cecilia Enriquez, Nathanaël |
| contents | We consider the typical Poisson-Voronoi cell in the Euclidean space R d and in particular the maximal distance D from a vertex of that cell to its nucleus. We provide a sharp asymptotics for the tail distribution of D. As a byproduct, we prove that the extremal index related to the sequence of such distances for all Voronoi cells included in a large box is equal to (2d) -1 . This confirms a conjecture formulated by Chenavier and Robert. The explicit constant appearing in the estimate of the tail probability of D is proved to be the mean volume of a random simplex formed by uniformly distributed points on the unit sphere conditioned on satisfying some spatial condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_11189 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sharp asymptotics for the maximal distance from the boundary to the nucleus of a typical Poisson-Voronoi cell Calka, Pierre d'Errico, Cecilia Enriquez, Nathanaël Probability We consider the typical Poisson-Voronoi cell in the Euclidean space R d and in particular the maximal distance D from a vertex of that cell to its nucleus. We provide a sharp asymptotics for the tail distribution of D. As a byproduct, we prove that the extremal index related to the sequence of such distances for all Voronoi cells included in a large box is equal to (2d) -1 . This confirms a conjecture formulated by Chenavier and Robert. The explicit constant appearing in the estimate of the tail probability of D is proved to be the mean volume of a random simplex formed by uniformly distributed points on the unit sphere conditioned on satisfying some spatial condition. |
| title | Sharp asymptotics for the maximal distance from the boundary to the nucleus of a typical Poisson-Voronoi cell |
| topic | Probability |
| url | https://arxiv.org/abs/2511.11189 |