On the geometry of random convex sets between polytopes and zonotopes

Alonso-Gutiérrez, David; Prochno, Joscha

Abstract

In this work we study a class of random convex sets that "interpolate" between polytopes and zonotopes. These sets arise from considering a qth-moment (q≥1) of an average of order statistics of 1-dimensional marginals of a sequence of N≥n independent random vectors in Rn. We consider the random model of isotropic log-concave distributions as well as the uniform distribution on an ℓnp-sphere (1≤p

Citation

Alonso-Gutiérrez, D., & Prochno, J. (2017). On the geometry of random convex sets between polytopes and zonotopes. Journal of mathematical analysis and applications, 450(1), 670-690. https://doi.org/10.1016/j.jmaa.2017.01.042

• Journal Article Type: Article
• Acceptance Date: Jul 31, 2016
• Online Publication Date: Jan 25, 2017
• Publication Date: Jun 1, 2017
• Deposit Date: Jun 28, 2018
• Publicly Available Date: Jul 6, 2018
• Journal: Journal of Mathematical Analysis and Applications
• Print ISSN: 0022-247X
• Electronic ISSN: 1096-0813
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 450
• Issue: 1
• Pages: 670-690
• DOI: https://doi.org/10.1016/j.jmaa.2017.01.042
• Keywords: Random convex body; Mean width; Orlicz norm; Isotropic log-concave measure; Cone measure
• Public URL: https://hull-repository.worktribe.com/output/899141
• Publisher URL: https://www.sciencedirect.com/science/article/pii/S0022247X17300744?via%3Dihub
• Additional Information: This article is maintained by: Elsevier; Article Title: On the geometry of random convex sets between polytopes and zonotopes; Journal Title: Journal of Mathematical Analysis and Applications; CrossRef DOI link to publisher maintained version: http://dx.doi.org/10.1016/j.jmaa.2017.01.042; Content Type: article; Copyright: © 2017 Elsevier Inc. All rights reserved.