Small ball probability and Dvoretzky theorem
Functional Analysis
2016-12-23 v1 Probability
Abstract
Large deviation estimates are by now a standard tool inthe Asymptotic Convex Geometry, contrary to small deviationresults. In this note we present a novel application of a smalldeviations inequality to a problem related to the diameters of random sections of high dimensional convex bodies. Our results imply an unexpected distinction between the lower and the upper inclusions in Dvoretzky Theorem.
Cite
@article{arxiv.math/0410001,
title = {Small ball probability and Dvoretzky theorem},
author = {Bo'az Klartag and Roman Vershynin},
journal= {arXiv preprint arXiv:math/0410001},
year = {2016}
}