Geodesic
Small ball probability estimates in terms of width
Rafał Latała 1   ; Krzysztof Oleszkiewicz 2
1 Institute of Mathematics Warsaw University Banacha 2 02-097 Warszawa, Poland
2 Institute of Mathematics Warsaw University Banacha 2 02-097 Warsaw, Poland
Studia Mathematica, Tome 169 (2005) no. 3, pp. 305-314 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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A certain inequality conjectured by Vershynin is studied. It is proved that for any symmetric convex body $K \subseteq {\mathbb R}^{n}$ with inradius $w$ and $\gamma_{n}(K) \leq 1/2$ we have $\gamma_{n}(sK) \leq (2s)^{w^{2}/4}\gamma_{n}(K)$ for any $s \in [0,1]$, where $\gamma_n$ is the standard Gaussian probability measure. Some natural corollaries are deduced. Another conjecture of Vershynin is proved to be false.
DOI : 10.4064/sm169-3-6
Keywords: certain inequality conjectured vershynin studied proved symmetric convex body subseteq mathbb inradius gamma leq have gamma leq gamma where gamma standard gaussian probability measure natural corollaries deduced another conjecture vershynin proved false

Rafał Latała  1   ; Krzysztof Oleszkiewicz  2

1 Institute of Mathematics Warsaw University Banacha 2 02-097 Warszawa, Poland
2 Institute of Mathematics Warsaw University Banacha 2 02-097 Warsaw, Poland 
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Rafał Latała; Krzysztof Oleszkiewicz. Small ball probability estimates in terms of width. Studia Mathematica, Tome 169 (2005) no. 3, pp. 305-314. doi: 10.4064/sm169-3-6

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