I have two sets of, respectively, N and M points, which are independently, randomly allocated on a sphere. I consider the Voronoi tessellation of the sphere by the N points, and I want to find how many of the other M points are on average in a Voronoi cell, and the standard deviation (or variance) of this number. As I am drawing point locations from a uniform distribution, I am thinking of looking at the statistics of Voronoi cell areas (first two moments), and then estimate accordingly the mean and variance of the density of points out of the M ones per cell. However, it looks like there is no analytical estimation of the PDF for cell area distribution for the spherical Voronoi tessellation. Any reference/suggestion that comes to mind? Otherwise, any alternative approach for the solution of my problem? I stress that I am looking for analytical solutions.