• 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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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

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

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

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


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.

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