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January 2008 Variance asymptotics and central limit theorems for generalized growth processes with applications to convex hulls and maximal points
T. Schreiber, J. E. Yukich
Ann. Probab. 36(1): 363-396 (January 2008). DOI: 10.1214/009117907000000259

Abstract

We show that the random point measures induced by vertices in the convex hull of a Poisson sample on the unit ball, when properly scaled and centered, converge to those of a mean zero Gaussian field. We establish limiting variance and covariance asymptotics in terms of the density of the Poisson sample. Similar results hold for the point measures induced by the maximal points in a Poisson sample. The approach involves introducing a generalized spatial birth growth process allowing for cell overlap.

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T. Schreiber. J. E. Yukich. "Variance asymptotics and central limit theorems for generalized growth processes with applications to convex hulls and maximal points." Ann. Probab. 36 (1) 363 - 396, January 2008. https://doi.org/10.1214/009117907000000259

Information

Published: January 2008
First available in Project Euclid: 28 November 2007

zbMATH: 1130.60031
MathSciNet: MR2370608
Digital Object Identifier: 10.1214/009117907000000259

Subjects:
Primary: 60F05
Secondary: 60D05

Rights: Copyright © 2008 Institute of Mathematical Statistics

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Vol.36 • No. 1 • January 2008
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