Incollection,
Statistics of Voronoi tilings
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 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.
