A central limit theorem for the Poisson-Voronoi approximation

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.