Small ball probability estimates in terms of width
Rafał Latała, 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 γn(K) ≤ 1/2 there is γn(sK) ≤ (2s)w2/4γn(K) for any s ∈ [0,1]. Some natural corollaries are deduced. Another conjecture of Vershynin is proved to be false.
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