On mean outer radii of random polytopes
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Other documents of the author: Alonso Gutiérrez, David; Nikos, Dafnis; Hernández Cifre, Maria Ángeles; Prochno, Joscha
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comunitat-uji-handle3:10234/8635
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Title
On mean outer radii of random polytopesDate
2014Publisher
Indiana University Mathematics JournalBibliographic citation
ALONSO-GUTIERREZ, David, et al. On mean outer radii of random polytopes. arXiv preprint arXiv:1211.2336, 2012.Type
info:eu-repo/semantics/articlePublisher version
http://www.iumj.indiana.edu/IUMJ/FULLTEXT/2014/63/5231Version
info:eu-repo/semantics/publishedVersionSubject
Abstract
In this paper we introduce a new sequence of quantities for random
polytopes. Let KN = conv{X1, . . . ,XN} be a random polytope generated by
independent random vectors uniformly distributed in an isotropic convex ... [+]
In this paper we introduce a new sequence of quantities for random
polytopes. Let KN = conv{X1, . . . ,XN} be a random polytope generated by
independent random vectors uniformly distributed in an isotropic convex body
K of Rn. We prove that the so-called k-th mean outer radius e Rk(KN) has
order max{
pk,plogN}LK with high probability if n2 N epn. We also
show that this is also the right order of the expected value of e Rk(KN) in the
full range n N epn. [-]
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On mean outer radii of random polytopes, Indiana Univ. Math. J. 63 (2014)Rights
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