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April 2009 Poisson–Voronoi approximation
Matthias Heveling, Matthias Reitzner
Ann. Appl. Probab. 19(2): 719-736 (April 2009). DOI: 10.1214/08-AAP561

Abstract

Let X be a Poisson point process and K⊂ℝd a measurable set. Construct the Voronoi cells of all points xX with respect to X, and denote by vX(K) the union of all Voronoi cells with nucleus in K. For K a compact convex set the expectation of the volume difference V(vX(K))−V(K) and the symmetric difference V(vX(KK) is computed. Precise estimates for the variance of both quantities are obtained which follow from a new jackknife inequality for the variance of functionals of a Poisson point process. Concentration inequalities for both quantities are proved using Azuma’s inequality.

Citation

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Matthias Heveling. Matthias Reitzner. "Poisson–Voronoi approximation." Ann. Appl. Probab. 19 (2) 719 - 736, April 2009. https://doi.org/10.1214/08-AAP561

Information

Published: April 2009
First available in Project Euclid: 7 May 2009

zbMATH: 1172.60003
MathSciNet: MR2521886
Digital Object Identifier: 10.1214/08-AAP561

Subjects:
Primary: 60D05
Secondary: 52A22, 60C05, 60G55

Rights: Copyright © 2009 Institute of Mathematical Statistics

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Vol.19 • No. 2 • April 2009
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