Mathematisches Seminar

Kolloquiumsvortrag Prof. Dr. Matthias Reitzner (Universität Osnabrück): "Poisson-Voronoi Approximation"

05.07.2013 von 16:15 bis 17:15

LMS 4, Raum 424

Einladender: Schütt

                                                                           

Abstract:

Let X  be a Poisson point process and K  a d-dimensional set. For a point x X  denote

   by vX (x) the Voronoi cell with respect to X , and set

                                                                                 v
X (K ) :=               vX (x
                                                                                                x
X K


which is the union of all Voronoi cells with center in K . We call vX (K ) the Poisson-Voronoi approximation of K .

In  this talk  the volume difference  Vd(vX (K )) Vd(K )  and the symmetric difference

Vd(vX (K )L::K ) are investigated. For K  a compact convex set estimates for the varian-

ce and limit theorems are obtained using the chaotic decomposition of these functions in

multiple Wiener-Ito integrals.

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