On the measure of Voronoi cells
| Autor: | Devroye, Luc, Györfi, László, Lugosi, Gábor, Walk, Harro |
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| Rok vydání: | 2015 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | $n$ 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. Comment: 19 pages |
| Databáze: | arXiv |
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