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Random convex hulls: a variance revisited

Part of: General convexity Geometric 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: [email protected]
∗∗ 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: [email protected]
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Abstract

An exact expression is determined for the asymptotic constant c2 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 2πc2n1/3.

Keywords

Convex hullrandom point setrandom polygonvariance

MSC classification

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