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On Mean Outer Radii of Random Polytopes

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

Authors

David Alonso-Gutiérrez

Nikos Dafnis

Maria Á Hernández Cifre

Joscha Prochno



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√.

Journal Article Type Article
Publication Date 2014
Journal Mathematics Journal
Print ISSN 0022-2518
Publisher Indiana University Mathematics Journal
Peer Reviewed Peer Reviewed
Volume 63
Issue 2
Pages 579-595
APA6 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
Publisher URL https://www.jstor.org/stable/24904230
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