The random version of Dvoretzky's theorem in ln∞

Abstract

We show that with "high probability" a section of the l n∞ ball of dimension κ ≤ cε log n (c > 0 a universal constant) is ε close to a multiple of the Euclidean ball in this section. We also show that, up to an absolute constant the estimate on k cannot be improved. © Springer-Verlag Berlin Heidelberg 2007.