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Abstract
Let K be an isotropic 1-unconditional convex body in ℝn. For every N > n consider N independent random points x1, . . . , xN uniformly distributed in K. We prove that, with probability greater than 1 – C1 exp(–cn) if N ≥ c1n and greater than 1 – C1 exp(–cn/ log n) if n < N < c1n, the random polytopes KN ≔ conv{±x1, . . . , ±xN} and SN ≔ conv{x1, . . . , xN} have isotropic constant bounded by an absolute constant C > 0.
Received: 2008-01-04
Published Online: 2010-03-10
Published in Print: 2010-April
© de Gruyter 2010
