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On the isotropic constant of random polytopes

2010
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Advances in Geometry
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Let K be an isotropic 1-unconditional convex body in R n . For every N > n consider N independent random points x1, . . . , xN uniformly distributed in K. We prove that, with probability greater than 1 − C 1 exp(−cn) if N ≥ c 1 n and greater than 1−C 1 exp(−cn/ log n) if n < N < c 1 n, the random polytopes KN := conv ± x1, . . . , ±xN and SN := conv{x1, . . . , xN } have isotropic constant bounded by an absolute constant C > 0.

doi:10.1515/advgeom.2010.009
fatcat:zdis7jziojblhacp4g2ca5jv4m