Mean width of random perturbations of random polytopes
نویسندگان
چکیده
منابع مشابه
On Mean Outer Radii of Random Polytopes
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 or...
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For a given convex body K in Rd, a random polytope K(n) is defined (essentially) as the intersection of n independent closed halfspaces containing K and having an isotropic and (in a specified sense) uniform distribution. We prove upper and lower bounds of optimal orders for the difference of the mean widths of K(n) and K as n tends to infinity. For a simplicial polytope P, a precise asymptotic...
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ژورنال
عنوان ژورنال: Advances in Geometry
سال: 2017
ISSN: 1615-7168,1615-715X
DOI: 10.1515/advgeom-2016-0032