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On the convex hull of n random points on a circle

Published online by Cambridge University Press:  14 July 2016

H. Carnal  and
J. Hüsler
H. Carnal
Affiliation:
University of Berne
J. Hüsler*
Affiliation:
University of Berne
*
∗Postal address for both authors: Department of Mathematical Statistics, Sidlerstr. 5, CH-3012 Berne, Switzerland.
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Abstract

We consider the convex hull of a sample of n randomly placed points in a unit circle. Obviously not all of the n points are needed to construct the convex hull. We show that asymptotically only the points belonging to a certain ring are used for the convex hull, where the size of the ring decreases at a certain rate such that the error of not completely correct construction of the convex hull by the particular subset of points tends to 0.

Keywords

STOCHASTIC GEOMETRYPOINTS ON A CIRCLE
Type
Short Communications
Information
Journal of Applied Probability , Volume 28 , Issue 1 , March 1991 , pp. 231 - 237
Copyright
Copyright © Applied Probability Trust 1991 

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References

Borgwardt, K. H., Gaffke, N., Jünger, M. and Reinelt, G. (1989) Computing the convex hull in the Euclidean plane in linear expected time. Technical Report 139, Universität Augsburg.Google Scholar
Carnal, H. (1970) Die konvexe Hülle von n rotationssymmetrisch verteilten Punkten. Z. Wahrscheinlichkeitsth. 15, 168–176.CrossRefGoogle Scholar
Eddy, W. F. (1980) The distribution of the convex hull of a Gaussian sample. J. Appl. Prob. 17, 686–695.Google Scholar
Eddy, W. F. and Gale, J. D. (1981) The convex hull of a spherically symmetric sample. Adv. Appl. Prob. 13, 751–763.CrossRefGoogle Scholar
Efron, B. (1965) The convex hull of a random set of points. Biometrika 52, 331–343.Google Scholar
Raynaud, H. (1965) Sur le comportement asymptotique de l'enveloppe convexe d'un nuage de points tirés au hasard dans Rn. C. R. Acad. Sci. Paris 261, 627–629.Google Scholar
Raynaud, H. (1970) Sur l'enveloppe convexe des nuages de points aléatoires dans Rn. J. Appl. Prob. 7, 35–48.Google Scholar
Renyi, A. and Sulanke, R. (1963) über die konvexe Hülle von n zufällig gewählten Punkten I. Z. Wahrscheinlichkeitsth. 2, 75–84.CrossRefGoogle Scholar
Renyi, A. and Sulanke, R. (1964) über die konvexe Hülle von n zufällig gewählten Punkten II. Z. Wahrscheinlichkeitsth. 3, 138–147.Google Scholar