A Central Limit Theorem for the Poisson-Voronoi Approximation

Abstract

For a compact convex set $K$ and a Poisson point process $\eta$, 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.

22 pages, modified references

References in corpus (2)

• Laws of large numbers in stochastic geometry with statistical applications
• Poisson--Voronoi approximation

Cited by in corpus (3)

• Fine Gaussian fluctuations on the Poisson space II: rescaled kernels, marked processes and geometric U-statistics
• Fine Gaussian fluctuations on the Poisson space, I: contractions, cumulants and geometric random graphs
• Portmanteau inequalities on the Poisson space: mixed regimes and multidimensional clustering