On the measure of Voronoi cells

2015/12/14 by Devroye, Luc, Györfi, László, Lugosi, Gábor +1 · 1 citation
#FOS: Mathematics #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.1512.04267

Abstract

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 ∈ 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.

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