Small ball probability and Dvoretzky's Theorem

B. Klartag*, R. Vershynin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

34 Scopus citations

Abstract

Large deviation estimates are by now a standard tool in Asymptotic Convex Geometry, contrary to small deviation results. In this note we present a novel application of a small deviations inequality to a problem that is related to the diameters of random sections of high dimensional convex bodies. Our results imply an unexpected distinction between the lower and upper inclusions in Dvoretzky's Theorem.

Original languageEnglish
Pages (from-to)193-207
Number of pages15
JournalIsrael Journal of Mathematics
Volume157
DOIs
StatePublished - Jan 2007
Externally publishedYes

Funding

FundersFunder number
National Science FoundationDMS-0111298, 0401032

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