Let X be a Poisson point process and K a convex set. For a point x in X denote by v(x) the Voronoi cell with respect to X, and by vX (K) the union of all Voronoi cells with center in K. We call vX(K) the Poisson-Voronoi approximation of K.

For K a compact convex set the volume difference Vd(vX(K))-Vd(K) and the symmetric difference Vd(vX(K) \triangle K) are investigated. Estimates for the variance and central limit theorems are obtained using the chaotic decomposition of these functions in multiple Wiener-Ito integrals. (Work in progress jointly with Matthias Schulte)