Indistinguishability of cells for the ideal Poisson Voronoi tessellation
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.
Fields of Study & Subjects
Point processes and geometric inequalities
Stochastic processes and statistical mechanics
Geometric Analysis and Curvature Flows
Publication details
- Journal / source
- Proceedings of the American Mathematical Society
- Volume
- 154
- Issue
- 4
- Pages
- 1589–1596
- Publication date
- 5 February 2026
- Language
- EN