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arXiv · 2408.10009

Indistinguishability of cells for the ideal Poisson Voronoi tessellation

Sam Mellick
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Abstract

In this note, we resolve a question of D'Achille, Curien, Enriquez, Lyons, and \"Unel 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.

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Sam Mellick. 2024-08-19. Indistinguishability of cells for the ideal Poisson Voronoi tessellation. https://arxiv.org/abs/2408.10009

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