%0 Journal Article
%T Small ball probability estimates in terms of width
%A Rafa£¿ Lata£¿a
%A Krzysztof Oleszkiewicz
%J Mathematics
%D 2005
%I arXiv
%R 10.4064/sm169-3-6
%X 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.
%U http://arxiv.org/abs/math/0501268v1