Year: 2011
Type: preprint
Abstract: For a compact convex set $K$ and a Poisson point process $η$, 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 so called Wiener-Itô chaos expansions and the central limit theorem is based on a more abstract central limit theorem for Poisson functionals, which is also derived.
Source: arXiv (Cornell University)
Author: Schulte, Matthias
Institution: Osnabrück University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2953362820