On Mean Outer Radii of Random Polytopes

Alonso-Gutiérrez, David; Dafnis, Nikos; Cifre, Maria Á Hernández; Prochno, Joscha

Abstract

In this paper we introduce a new sequence of quantities for random polytopes. Let $K_N=\conv\{X_1,...,X_N\}$ be a random polytope generated by independent random vectors uniformly distributed in an isotropic convex body K of $\R^n$. We prove that the so-called k-th mean outer radius R˜k(KN) has order max{k−−√,logN−−−−−√}LK with high probability if n2≤N≤en√. We also show that this is also the right order of the expected value of R˜k(KN) in the full range n≤N≤en√.

Citation

Alonso-Gutiérrez, D., Dafnis, N., Cifre, M. Á. H., & Prochno, J. (2014). On Mean Outer Radii of Random Polytopes. Indiana University Mathematics Journal, 63(2), 579-595

• Journal Article Type: Article
• Acceptance Date: Jan 1, 2014
• Publication Date: 2014
• Deposit Date: Jun 29, 2018
• Journal: Mathematics Journal
• Print ISSN: 0022-2518
• Publisher: Indiana University Mathematics Journal
• Peer Reviewed: Peer Reviewed
• Volume: 63
• Issue: 2
• Pages: 579-595
• Public URL: https://hull-repository.worktribe.com/output/901503
• Publisher URL: https://www.jstor.org/stable/24904230