@incollection{statphys23_0498,
title = {Statistics of Voronoi tilings},
address = {Genova, Italy},
author = {H.J. Hilhorst},
booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics},
editor = {Luciano Pietronero and Vittorio Loreto and Stefano Zapperi},
month = {9-13 July},
url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=498},
year = {2007},
abstract = {The Voronoi diagram is an idealized concept in random geometry. It partitions a space occupied by point-particles into cells in such a manner that each generic point of space is in the cell of the particle to which it is closest. The Voronoi diagram serves, among other things, as a reference system for analyzing
experimental data on cellular structures. Such data in turn obey empirical laws that were formulated by Lewis, Aboav-Weaire, and others.
New exact results on planar Voronoi diagrams will be presented. These
(i) provide an understanding of the statistics of $n$-sided cells in the
large-$n$ limit;
(ii) make it possible to Monte Carlo generate rare events that had so far been
inaccessible to simulations;
and (iii) enable us to examine the validity of the empirical laws within
the framework of a large-$n$ expansion.},
keywords = {aboav-weaire cells exact law methods montecarlo planar results statphys23 topic-4 voronoi }
}
::