Small ball probability estimates in terms of width

Details Small ball probability estimates in terms of width Small ball probability estimates in terms of width

2005-01-18

arxiv.org/abs/math/0501268v1

Mathematics

Probability

10 pages

Scientific paper

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.

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