On the approximation of a polytope by its dual L_p-centroid bodies

2011/07/19 by Grigoris Paouris, Paouris, Grigoris, Elisabeth M. Werner +1
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #math.FA

paper · pdf · doi:10.48550/arxiv.1107.3683

arxiv created 2011/07/19 · arxiv updated 2011/07/20

Abstract

We show that the rate of convergence on the approximation of volumes of a convex symmetric polytope P in Rⁿ by its dual L_p-centroid bodies is independent of the geometry of P. In particular we show that if P has volume 1, lim_{p→ ∞} \fracplogp (\frac|Z_p^∘(P)||P^∘| -1) = n². We provide an application to the approximation of polytopes by uniformly convex sets.

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