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

Pierre Calka, Tomasz Schreiber

Type: Article

Publication Date: 2006-03-01

Citations: 7

DOI: https://doi.org/10.1017/s0001867800000793

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 R d . 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.

Locations

Advances in Applied Probability - View - PDF
HAL (Le Centre pour la Communication Scientifique Directe) - View

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Action	Title	Year	Authors
+ PDF Chat	�ber die konvexe H�lle von n zuf�llig gew�hlten Punkten	1963	A. R�nyi Robert A. Sulanke
+	Random polytopes and the Efron--Stein jackknife inequality	2003	Matthias Reitzner
+	On the LLN for the number of vertices of a random convex hull	2000	Bruno Massé
+ PDF Chat	Convex bodies, economic cap coverings, random polytopes	1988	Imre Bárány D. G. Larman
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+ PDF Chat	Limit theorems for convex hulls	1988	Piet Groeneboom
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+	Random polytopes in a ball	1984	Christian Buchta Josef S. Müller