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On mean outer radii of random polytopes | | David Alonso-Gutierrez
; Nikos Dafnis
; Maria A. Hernandez Cifre
; Joscha Prochno
; | | Date: |
10 Nov 2012 | | 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 $widetilde R_k(K_N)$ has
order $max{sqrt{k},sqrt{log N}}L_K$ with high probability if $n^2leq
Nleq e^{sqrt{n}}$. We also show that this is also the right order of the
expected value of $widetilde R_k(K_N)$ in the full range $nleq Nleq
e^{sqrt{n}}$. | | Source: | arXiv, 1211.2336 | | Services: | Forum | Review | PDF | Favorites | |
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