Laboratoire de Mathématiques Raphaël Salem

UMR 6085 CNRS - University of Rouen Normandy

We employ stabilization methods in the context of Malliavin-Stein theory to establish rates of multivariate normal convergence for a large class of vectors $$(H_s^{(1)},...,H_s^{(m)}), \ s \geq 1,$$ of marked Poisson point processes in Euclidean space, as the intensity parameter $s \to \infty$. The rates are in terms of the $d_2$ and $d_3$ distances, a generalized multivariate Kolmogorov distance, rates are unimprovable. We use the general results to deduce presumably optimal rates of multivariate normal convergence for statistics arising in random graphs and topological data analysis as well as for multivariate statistics used to test equality of distributions. This is based on joint work with M. Schulte