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.