Normal approximation of geometric Poisson functionals

Last, G., Karlsruhe Institute of Technology, Germany

We consider functionals of a (possibly marked) stationary spatial Poisson processes. Recent progress on Stein's method shows how to use stochastic analysis on Poisson spaces for bounding the Wasserstein and the Kolmogorov distance between the distribution of a Poisson functional (suitably normalized) and the standard normal distribution in terms of Malliavin operators. In the first part of this talk we show that this method can be successfully applied to the intrinsic volumes (and more general additive functionals) of the Boolean model and of intersection processes of Poisson hyperplanes. In the second part we will apply a second order Poincare inequality involving only first and second order differential operators to the Poisson-Voronoi tessellation and nearest neighbour graphs. This talk is based on joint work with Daniel Hug, Giovanni Peccati, Mathew Penrose Matthias Schulte and Christoph Thaele.