Electronic Communications in Probability

Concentration of random polytopes around the expected convex hull

Daniel Fresen and Richard Vitale

Full-text: Open access

Abstract

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.

Article information

Source
Electron. Commun. Probab., Volume 19 (2014), paper no. 59, 8 pp.

Dates
Accepted: 26 August 2014
First available in Project Euclid: 7 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465316761

Digital Object Identifier
doi:10.1214/ECP.v19-3376

Mathematical Reviews number (MathSciNet)
MR3254738

Zentralblatt MATH identifier
1314.60044

Subjects
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

Keywords
random polytope law of large numbers log-concave expected convex hull floating body

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

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


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