Open Access
November 2016 Asymptotic theory for statistics of the Poisson–Voronoi approximation
Christoph Thäle, J.E. Yukich
Bernoulli 22(4): 2372-2400 (November 2016). DOI: 10.3150/15-BEJ732


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.


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Christoph Thäle. J.E. Yukich. "Asymptotic theory for statistics of the Poisson–Voronoi approximation." Bernoulli 22 (4) 2372 - 2400, November 2016.


Received: 1 December 2014; Revised: 1 April 2015; Published: November 2016
First available in Project Euclid: 3 May 2016

zbMATH: 1356.60020
MathSciNet: MR3498032
Digital Object Identifier: 10.3150/15-BEJ732

Keywords: combinatorial geometry , Poisson point process , Poisson–Voronoi approximation , random mosaic , stabilizing functional , Stochastic geometry

Rights: Copyright © 2016 Bernoulli Society for Mathematical Statistics and Probability

Vol.22 • No. 4 • November 2016
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