Asymptotics for Voronoi tessellations on random samples
The paper describes the asymptotic behavior of total edge length of a Voronoi tessellation in the plane generated by random point set in the unit square. The main result is formulated in terms of complete convergence for an arbitrary common continuous density of independent generating points. Using the theory of subadditive and superadditive Euclidean functionals it extends substantially Miles' (1970) asymptotics. Remarks concerning the Delaunay triangulations conclude the paper.
scientific article; zbMATH DE number 1792541