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Small ball probability and Dvoretzky theorem

Bo'az Klartag·Roman Vershynin
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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.

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Bo'az Klartag, Roman Vershynin. 2004-09-30. Small ball probability and Dvoretzky theorem. https://arxiv.org/abs/math/0410001

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