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Random convex hulls: a variance revisited

Part of:General convexityGeometric probability and stochastic geometry

Published online by Cambridge University Press:  01 July 2016

Steven Finch and
Irene Hueter
Steven Finch*
Affiliation:
Clay Mathematics Institute
Irene Hueter*
Affiliation:
City University of New York, Baruch College, and University of Massachusetts Boston
*
∗ Postal address: Clay Mathematics Institute, One Bow Street, Cambridge, MA 02138, USA. Email address: steven.finch@inria.fr
∗∗ Postal address: Department of Mathematics, Baruch College, City University of New York, Box B6-230, One Bernard Baruch Way, New York, NY 10010, USA. Email address: irene_hueter@baruch.cuny.edu
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Abstract

An exact expression is determined for the asymptotic constant c 2 in the limit theorem by P. Groeneboom (1988), which states that the number of vertices of the convex hull of a uniform sample of n random points from a circular disk satisfies a central limit theorem, as n → ∞, with asymptotic variance 2πc 2 n 1/3.

Keywords

Convex hullrandom point setrandom polygonvariance

MSC classification

Primary:52A22: Random convex sets and integral geometry
Secondary:60D05: Geometric probability and stochastic geometry

Information

Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 36 , Issue 4 , December 2004, pp. 981 - 986
Copyright
Copyright © Applied Probability Trust 2004 

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Footnotes

Partially supported by a Clay Book Fellowship.

Partially supported by PSC-CUNY grant no. 60032-33-34.

References

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