The Annals of Probability
- Ann. Probab.
- Volume 36, Number 1 (2008), 363-396.
Variance asymptotics and central limit theorems for generalized growth processes with applications to convex hulls and maximal points
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.
Ann. Probab., Volume 36, Number 1 (2008), 363-396.
First available in Project Euclid: 28 November 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60F05: Central limit and other weak theorems
Secondary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65]
Schreiber, T.; Yukich, J. E. Variance asymptotics and central limit theorems for generalized growth processes with applications to convex hulls and maximal points. Ann. Probab. 36 (2008), no. 1, 363--396. doi:10.1214/009117907000000259. https://projecteuclid.org/euclid.aop/1196268683