BARANY, I;
LARMAN, DG;
(1988)
CONVEX-BODIES, ECONOMIC CAP COVERINGS, RANDOM POLYTOPES.
MATHEMATIKA
, 35
(70)
274 - 291.
10.1112/S0025579300015266.
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Abstract
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).
| Type: | Article |
|---|---|
| Title: | CONVEX-BODIES, ECONOMIC CAP COVERINGS, RANDOM POLYTOPES |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1112/S0025579300015266 |
| Publisher version: | http://dx.doi.org/10.1112/S0025579300015266 |
| Language: | English |
| Additional information: | © 1988 Cambridge University Press |
| Keywords: | 52A22: CONVEX SETS AND RELATED GEOMETRIC TOPICS, Random convex sets and integral geometry |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/141935 |
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