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Indistinguishability of cells for the ideal Poisson Voronoi tessellation

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arxiv 2408.10009 v3 pith:KC7QHVFT submitted 2024-08-19 math.PR math.DS

Sam Mellick This is my paper · ORCID
classification math.PRmath.DS
keywords poissontheoremcellsidealmeyerovitchtessellationvoronoiachille
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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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  1. Ideal Poisson--Voronoi tessellations beyond hyperbolic spaces

    math.PR 2024-12 conditional novelty 6.0 of 10

    The low-intensity Poisson-Voronoi tessellation of H2 × H2 with the L1 metric converges to an isometry-invariant ideal tessellation whose cell ends are unions of boundary circles, and equal-separation loci between coro...

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