Advances in Applied Probability

Large deviation probabilities for the number of vertices of random polytopes in the ball

Pierre Calka and Tomasz Schreiber

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Abstract

In this paper we establish large deviation results on the number of extreme points of a homogeneous Poisson point process in the unit ball of Rd. In particular, we deduce an almost-sure law of large numbers in any dimension. As an auxiliary result we prove strong localization of the extreme points in an annulus near the boundary of the ball.

Article information

Source
Adv. in Appl. Probab. Volume 38, Number 1 (2006), 47-58.

Dates
First available in Project Euclid: 1 April 2006

Permanent link to this document
http://projecteuclid.org/euclid.aap/1143936139

Digital Object Identifier
doi:10.1239/aap/1143936139

Mathematical Reviews number (MathSciNet)
MR2213963

Zentralblatt MATH identifier
05033685

Subjects
Primary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65]
Secondary: 60F10: Large deviations

Keywords
Convex hull covering of the sphere large deviation measure concentration random polytope

Citation

Calka, Pierre; Schreiber, Tomasz. Large deviation probabilities for the number of vertices of random polytopes in the ball. Adv. in Appl. Probab. 38 (2006), no. 1, 47--58. doi:10.1239/aap/1143936139. http://projecteuclid.org/euclid.aap/1143936139.


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