On Mean Outer Radii of Random Polytopes

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 2014 Mathematics Journal 0022-2518 Indiana University Mathematics Journal Peer Reviewed 63 2 579-595 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 https://www.jstor.org/stable/24904230
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