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Convex bodies, economic cap coverings, random polytopes

Part of:General convexity

Published online by Cambridge University Press:  26 February 2010

I. Bárány and
D. G. Larman
I. Bárány
Affiliation:
The Mathematical Institute of the Hungarian Academy of Sciences, 1365 Budapest, P.O.B. 127, Hungary
D. G. Larman
Affiliation:
Department of Mathematics, University College London, Gower Street, London, WC1E 6BT
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Let K be a convex compact body with nonempty interior in the d-dimensional Euclidean space Rd and let x1, …, xn be random points in K, independently and uniformly distributed. Define Kn = conv {x1, …, xn}. Our main concern in this paper will be the behaviour of the deviation of vol Kn from vol K as a function of n, more precisely, the expectation of the random variable vol (K\Kn). We denote this expectation by E (K, n).

MSC classification

Secondary:52A22: Random convex sets and integral geometry

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Type
Research Article
Information
Mathematika , Volume 35 , Issue 2 , December 1988, pp. 274 - 291
Copyright
Copyright © University College London 1988

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