On the Gaussian behavior of marginals and the mean width of random polytopes

Abstract

© 2014 American Mathematical Society. We show that the expected value of the mean width of a random polytope generated by N random vectors (n ≤ N ≤ e√n) uniformly distributed in an isotropic convex body in ℝnis of the order√logNLK. This completes a result of Dafnis, Giannopoulos and Tsolomitis. We also prove some results in connection with the 1-dimensional marginals of the uniform probability measure on an isotropic convex body, extending the interval in which the average of the distribution functions of those marginals behaves in a sub- or supergaussian way.