New Monte Carlo method for planar Poisson-Voronoi cells
Abstract
By a new Monte Carlo algorithm we evaluate the sidedness probability p_n of a planar Poisson-Voronoi cell in the range 3 \leq n \leq 1600. The algorithm is developed on the basis of earlier theoretical work; it exploits, in particular, the known asymptotic behavior of p_n as n\to\infty. Our p_n values all have between four and six significant digits. Accurate n dependent averages, second moments, and variances are obtained for the cell area and the cell perimeter. The numerical large n behavior of these quantities is analyzed in terms of asymptotic power series in 1/n. Snapshots are shown of typical occurrences of extremely rare events implicating cells of up to n=1600 sides embedded in an ordinary Poisson-Voronoi diagram. We reveal and discuss the characteristic features of such many-sided cells and their immediate environment. Their relevance for observable properties is stressed.
Cite
@article{arxiv.cond-mat/0612422,
title = {New Monte Carlo method for planar Poisson-Voronoi cells},
author = {H. J. Hilhorst},
journal= {arXiv preprint arXiv:cond-mat/0612422},
year = {2015}
}
Comments
35 pages including 10 figures and 4 tables