Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 19 (2014), paper no. 59, 8 pp.
Concentration of random polytopes around the expected convex hull
We provide a streamlined proof and improved estimates for the weak multivariate Gnedenko law of large numbers on concentration of random polytopes within the space of convex bodies (in a fixed or a high dimensional setting), as well as a corresponding strong law of large numbers.
Electron. Commun. Probab., Volume 19 (2014), paper no. 59, 8 pp.
Accepted: 26 August 2014
First available in Project Euclid: 7 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65]
Secondary: 60F05: Central limit and other weak theorems 60F15: Strong theorems 52A20: Convex sets in n dimensions (including convex hypersurfaces) [See also 53A07, 53C45] 52A22: Random convex sets and integral geometry [See also 53C65, 60D05] 52A23: Asymptotic theory of convex bodies [See also 46B06] 53A27 52B11: $n$-dimensional polytopes
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Fresen, Daniel; Vitale, Richard. Concentration of random polytopes around the expected convex hull. Electron. Commun. Probab. 19 (2014), paper no. 59, 8 pp. doi:10.1214/ECP.v19-3376. https://projecteuclid.org/euclid.ecp/1465316761