Statistics of Random Plane Voronoi Tessellations

If S is a discrete set of points in a space, and each point of the space is associated with the nearest point of S, then the resulting partition is called a Voronoi tessellation. This paper derives a general scheme for setting up integrals for statistics for tessellations generated from a Poisson point process. For the case of the plane, the integrals are evaluated to find the variances of cell area, edge length, perimeter, and number of sides. The distributions of several parameters, including edge length, are also found.