Bernoulli

• Bernoulli
• Volume 22, Number 4 (2016), 2372-2400.

Asymptotic theory for statistics of the Poisson–Voronoi approximation

Abstract

This paper establishes expectation and variance asymptotics for statistics of the Poisson–Voronoi approximation of general sets, as the underlying intensity of the Poisson point process tends to infinity. Statistics of interest include volume, surface area, Hausdorff measure, and the number of faces of lower-dimensional skeletons. We also consider the complexity of the so-called Voronoi zone and the iterated Voronoi approximation. Our results are consequences of general limit theorems proved with an abstract Steiner-type formula applicable in the setting of sums of stabilizing functionals.

Article information

Source
Bernoulli, Volume 22, Number 4 (2016), 2372-2400.

Dates
Revised: April 2015
First available in Project Euclid: 3 May 2016

https://projecteuclid.org/euclid.bj/1462297684

Digital Object Identifier
doi:10.3150/15-BEJ732

Mathematical Reviews number (MathSciNet)
MR3498032

Zentralblatt MATH identifier
1356.60020

Citation

Thäle, Christoph; Yukich, J.E. Asymptotic theory for statistics of the Poisson–Voronoi approximation. Bernoulli 22 (2016), no. 4, 2372--2400. doi:10.3150/15-BEJ732. https://projecteuclid.org/euclid.bj/1462297684

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