Variance asymptotics and central limit theorems for generalized growth processes with applications to convex hulls and maximal points

Details Variance asymptotics and central limit theorems for generalized growth processes with applications to convex hulls and maximal points Variance asymptotics and central limit theorems for generalized growth processes with applications to convex hulls and maximal points

2007-02-19

arxiv.org/abs/math/0702553v2

Annals of Probability 2008, Vol. 36, No. 1, 363-396

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/009117907000000259 the Annals of Probability (http://www.imstat.org/aop/) by the Ins

Scientific paper

10.1214/009117907000000259

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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