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Small ball probability estimates in terms of width

Rafał Latała·Krzysztof Oleszkiewicz
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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.

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Rafał Latała, Krzysztof Oleszkiewicz. 2005-01-18. Small ball probability estimates in terms of width. https://doi.org/10.4064/sm169-3-6

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