Article,
On the size distribution of Poisson-Voronoi cells
Physica A-Statistical Mechanics And Its Applications, 385 (2): 518-526 (2007)
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 (3D) spaces there is no exact result
known for the size distribution of Voronoi cells. Motivated by the
simple form of the distribution function in the ID case, a simple
and compact analytical formula is proposed for approximating the
Voronoi cell's size-distribution function in the practically important
2D and 3D cases as well. Denoting the dimensionality of the space
by d (d = 1, 2, 3) the f (y) = Const * y (3(d-1))(/2) exp(-(3d
+ 1)y/2) compact form is suggested for the normalized cell-size distribution
function. By using large-scale computer simulations the viability
of the proposed distribution function is studied and critically discussed.
(C) 2007 Elsevier B.V. All rights reserved.
