Asymptotic statistics of then-sided planar Poisson–Voronoi cell: II. Heuristics

We develop a set of heuristic arguments to explain several results on planar Poisson-Voronoi tessellations that were derived earlier at the cost of considerable mathematical effort.The results concern Voronoi cells having a large number n of sides.The arguments start from an entropy balance applied to the arrangement of n neighbors around a central cell.This is followed by a simplified evaluation of the phase space integral for the probability p n that an arbitrary cell be n-sided.The limitations of the arguments are indicated.As a new application we calculate the expected number of Gabriel (or full) neighbors of an n-sided cell in the large-n limit.