This is an announcement for the paper "Small ball probability estimates in terms of width" by Rafal Latal and Krzysztof Oleszkiewicz.

Abstract: A certain inequality conjectured by Vershynin is studied. It is proved that for any $n$-dimensional symmetric convex body $K$ with inradius $w$ and $\gamma_{n}(K) \leq 1/2$ there is $\gamma_{n}(sK) \leq (2s)^{w^{2}/4}\gamma_{n}(K)$ for any $s \in [0,1]$. Some natural corollaries are deduced. Another conjecture of Vershynin is proved to be false.

Archive classification: Probability; Functional Analysis

Mathematics Subject Classification: 60G15, 60E15

Remarks: 10 pages

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Submitted from: rlatala@mimuw.edu.pl

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