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.
Keywords
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}
}