On the Geometry of Random Polytopes

Abstract

We present a simple proof to a fact recently established in Guedon et al. (Commun Contemp Math (to appear, 2018). arXiv:1811.12007): let xi be a symmetric random variable that has variance 1, let Gamma = (xi(ij)) be an N x n random matrix whose entries are independent copies of xi, and set X-1,..., X-N to be the rows of Gamma. Then under minimal assumptions on. and as long as N >= c(1)n, with high probability c(2) (B-infinity(n) boolean AND root log(eN/n)B-2(n) subset of absconv(X-1,..., X-N). Show more