%0 Journal Article
%T On the measure of Voronoi cells
%A Luc Devroye
%A L¨¢szl¨® Gy£¿rfi
%A G¨¢bor Lugosi
%A Harro Walk
%J Statistics
%D 2015
%I arXiv
%X $n$ independent random points drawn from a density $f$ in $R^d$ define a random Voronoi partition. We study the measure of a typical cell of the partition. We prove that the asymptotic distribution of the probability measure of the cell centered at a point $x \in R^d$ is independent of $x$ and the density $f$. We determine all moments of the asymptotic distribution and show that the distribution becomes more concentrated as $d$ becomes large. In particular, we show that the variance converges to zero exponentially fast in $d$. %We also study the measure of the largest cell of the partition. %{\red We also obtain a density-free bound for the rate of convergence of the diameter of a typical Voronoi cell.
%U http://arxiv.org/abs/1512.04267v1