Παρασκευή 12 Νοεμβρίου. Ώρα 1:10μμ. Αίθουσα Α32, Μαθηματικό ΕΚΠΑ

Ομιλητής: Αναστάσης Μπάτσης (Ruhr-University Bochum)

Τίτλος: Weak convergence of the intersection process of Poisson hyperplanes

Περίληψη:

The mathematical analysis of Poisson hyperplane processes and the resulting random tessellations has a long tradition in stochastic geometry. In this talk, we focus on the intersection point process induced by a stationary and isotropic Poisson hyperplane process where only hyperplanes that intersect a centered ball of radius R > 0 are considered. Taking R = t^{−d/(d+1)}, it is shown that this point process converges in distribution, as t → ∞, to a Poisson point process on R^d \ {0}. A bound on the speed of convergence in terms of the Kantorovich-Rubinstein distance is provided as well.
Implications on the weak convergence of the convex hull of the intersection point process and the convergence of its f-vector will be also discussed, disproving and correcting thereby a conjecture of Devroye and Toussaint [J. Algorithms 14.3 (1993), 381–394].