High dimensional random sections of isotropic convex bodies |
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Authors: | David Alonso-Gutiérrez Grigoris Paouris |
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Institution: | a Departamento de Matemáticas, Universidad de Zaragoza, 50009 Zaragoza, Spain b Department of Mathematics, Texas A & M University, College Station, TX 77843, USA |
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Abstract: | We study two properties of random high dimensional sections of convex bodies. In the first part of the paper we estimate the central section function for random F∈Gn,k and K⊂Rn a centrally symmetric isotropic convex body. This partially answers a question raised by V.D. Milman and A. Pajor (see V.D. Milman, A. Pajor, Isotropic positions and inertia ellipsoids and zonoids of the unit ball of a normed n-dimensional space, in: Lecture Notes in Math., vol. 1376, Springer, 1989, p. 88]). In the second part we show that every symmetric convex body has random high dimensional sections F∈Gn,k with outer volume ratio bounded by |
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Keywords: | Isotropic convex bodies Section function M-position |
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