Elsevier

Advances in Applied Mathematics

Volume 49, Issues 3–5, September–October 2012, Pages 285-306
Advances in Applied Mathematics

A central limit theorem for the Poisson–Voronoi approximation

https://doi.org/10.1016/j.aam.2012.08.001Get rights and content
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Abstract

For a compact convex set K and a Poisson point process ηλ, the union of all Voronoi cells with a nucleus in K is the Poisson–Voronoi approximation of K. Lower and upper bounds for the variance and a central limit theorem for the volume of the Poisson–Voronoi approximation are shown. The proofs make use of the so-called Wiener–Itô chaos expansion and the central limit theorem is based on a more abstract central limit theorem for Poisson functionals, which is also derived.

MSC

primary
60D05
60F05
secondary
60G55
60H07

Keywords

Central limit theorem
Poisson point process
Poisson–Voronoi approximation
Random tessellation
Set reconstruction
Stochastic geometry
Wiener–Itô chaos expansion

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