On Mean Outer Radii of Random Polytopes
نویسنده
چکیده
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 R. We prove that the so-called k-th mean outer radius R̃k(KN ) has order max{ √ k, √ logN}LK with high probability if n ≤ N ≤ e √ . We also show that this is also the right order of the expected value of R̃k(KN ) in the full range n ≤ N ≤ e √
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