English

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}
}