Asymptotic statistics of the n-sided planar Voronoi cell: II. Heuristics

Details Asymptotic statistics of the n-sided planar Voronoi cell: II. Heuristics Asymptotic statistics of the n-sided planar Voronoi cell: II. Heuristics

2009-03-20

arxiv.org/abs/0903.3466v1

J. Stat. Mech. (2009) P05007

Physics

Condensed Matter

Statistical Mechanics

22 pages, 10 figures

Scientific paper

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. It 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.

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