On the sizedistribution of Poisson Voronoi cells
Abstract
Poisson Voronoi diagrams are useful for modeling and describing various natural patterns and for generating random lattices. Although this particular space tessellation is intensively studied by mathematicians, in two and three dimensional spaces there is no exact result known for the sizedistribution of Voronoi cells. Motivated by the simple form of the distribution function in the onedimensional case, a simple and compact analytical formula is proposed for approximating the Voronoi cell's size distribution function in the practically important two and three dimensional cases as well. Denoting the dimensionality of the space by d (d=1,2,3) the $f(y)=Const*y^{(3d1)/2}exp((3d+1)y/2)$ compact form is suggested for the normalized cellsize distribution function. By using largescale computer simulations the validity of the proposed distribution function is studied and critically discussed.
 Publication:

arXiv eprints
 Pub Date:
 June 2004
 arXiv:
 arXiv:condmat/0406116
 Bibcode:
 2004cond.mat..6116J
 Keywords:

 Condensed Matter  Soft Condensed Matter;
 Condensed Matter  Statistical Mechanics
 EPrint:
 12 pages, 6 figures