Indistinguishability of cells for the ideal Poisson Voronoi tessellation
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913563294040064 |
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| author | Mellick, Sam |
| author_facet | Mellick, Sam |
| contents | In this note, we resolve a question of D'Achille, Curien, Enriquez, Lyons, and Ünel by showing that the cells of the ideal Poisson Voronoi tessellation are indistinguishable. This follows from an application of the Howe-Moore theorem and a theorem of Meyerovitch about the nonexistence of thinnings of the Poisson point process. We also give an alternative proof of Meyerovitch's theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_10009 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Indistinguishability of cells for the ideal Poisson Voronoi tessellation Mellick, Sam Probability Dynamical Systems In this note, we resolve a question of D'Achille, Curien, Enriquez, Lyons, and Ünel by showing that the cells of the ideal Poisson Voronoi tessellation are indistinguishable. This follows from an application of the Howe-Moore theorem and a theorem of Meyerovitch about the nonexistence of thinnings of the Poisson point process. We also give an alternative proof of Meyerovitch's theorem. |
| title | Indistinguishability of cells for the ideal Poisson Voronoi tessellation |
| topic | Probability Dynamical Systems |
| url | https://arxiv.org/abs/2408.10009 |