On the isotropic constant of random polytopes

Let K be an isotropic 1-unconditional convex body in ℝ n . For every N > n consider N independent random points x 1, . . . , x N 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{±x 1, . . . , ±x N } and SN ≔ conv{x 1, . . . , x N } have isotropic constant bounded by an absolute constant C > 0.