Lectures on Random Voronoi Tessellations

angle arbitrary Borel set boundary centroid contains convex d-n+k d-polytope defined Delaunay cells Delaunay edges Delaunay tessellation denotes density dyd-n equivariant Exercise facets Figure formula Fubini's theorem Gabriel neighbours Hadwiger's theorem hard core homogeneous Poisson process implies integral geometry intensity intersection invariant under translations isotropic k-dimensional k-facets k-flat L₂ Lecture Notes Lemma locally finite Mathematical measurable function measure theory Models Møller non-negative measurable function nuclei nullset obtain Palm distribution Palm measure planar section planar Voronoi point process Poisson point process Poisson-Voronoi cell Poisson-Voronoi tessellation polytope Proposition 3.2.3 random Voronoi tessellations Remark simulated spatial point processes spatial Voronoi Springer-Verlag stationary stochastic geometry tessella tion topological regular translation invariant typical Poisson-Delaunay cell typical Poisson-Voronoi typical Voronoi cell vertex void-probabilities Voronoi and Delaunay Voronoi tessellation Ε Σ ΕΦ