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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

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