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CONVEX-BODIES, ECONOMIC CAP COVERINGS, RANDOM POLYTOPES

BARANY, I; LARMAN, DG; (1988) CONVEX-BODIES, ECONOMIC CAP COVERINGS, RANDOM POLYTOPES. MATHEMATIKA , 35 (70) 274 - 291. 10.1112/S0025579300015266. Green open access

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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 > 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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