Bernoulli

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

Asymptotic theory for statistics of the Poisson–Voronoi approximation

Christoph Thäle and J.E. Yukich

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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
Received: December 2014
Revised: April 2015
First available in Project Euclid: 3 May 2016

Permanent link to this document
https://projecteuclid.org/euclid.bj/1462297684

Digital Object Identifier
doi:10.3150/15-BEJ732

Mathematical Reviews number (MathSciNet)
MR3498032

Zentralblatt MATH identifier
06603448

Keywords
combinatorial geometry Poisson point process Poisson–Voronoi approximation random mosaic stabilizing functional stochastic geometry

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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