What question did this study set out to answer?

The research aims to demonstrate that the cells formed by the ideal Poisson Voronoi tessellation are indistinguishable.

February 8, 2026

Indistinguishability of cells for the ideal Poisson Voronoi tessellation

Key Points

The research aims to demonstrate that the cells formed by the ideal Poisson Voronoi tessellation are indistinguishable.
Applied the Howe-Moore theorem to the Poisson Voronoi tessellation.
Utilized Meyerovitch’s theorem regarding the nonexistence of thinnings of the Poisson point process.
Provided an alternative proof for Meyerovitch’s theorem.
Confirmed that the cells of the ideal Poisson Voronoi tessellation are indistinguishable from one another.
Established a connection between properties of stochastic processes and tessellation characteristics.

Abstract

In this note, we resolve a question of D’Achille, Curien, Enriquez, Lyons, and Ünel arXiv:2303.16831 [math.PR , 2023] 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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