1Institute of Mathematics Warsaw University Banacha 2 02-097 Warszawa, Poland 2Institute of Mathematics Warsaw University Banacha 2 02-097 Warsaw, Poland
Studia Mathematica, Tome 169 (2005) no. 3, pp. 305-314
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.
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
Affiliations des auteurs :
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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title = {Small ball probability estimates in terms of width},
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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
