Poissonian and non-Poissonian Voronoi diagrams with application to the aggregation of molecules

The distributions that regulate the spatial domains of the Poissonian Voronoi diagrams are discussed adopting the sum of gamma variate of argument two. The distributions that arise from the product and quotient of two gamma variates of argument two are also derived. Three examples of non-Poissonian seeds for the Voronoi Diagrams are discussed. The developed algorithm allows the simulation of an aggregation of methanol and water.