Small ball probability estimates in terms of width
Rafał Latała ; Krzysztof Oleszkiewicz
Studia Mathematica, Tome 166 (2005), p. 305-314 / Harvested from The Polish Digital Mathematics Library
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A certain inequality conjectured by Vershynin is studied. It is proved that for any symmetric convex body K ⊆ ℝⁿ with inradius w and γₙ(K) ≤ 1/2 we have γₙ(sK)≤(2s)w²/4γₙ(K) for any s ∈ [0,1], where γₙ is the standard Gaussian probability measure. Some natural corollaries are deduced. Another conjecture of Vershynin is proved to be false.

Publié le : 2005-01-01
EUDML-ID : urn:eudml:doc:285251 
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Rafał Latała; Krzysztof Oleszkiewicz. Small ball probability estimates in terms of width. Studia Mathematica, Tome 166 (2005) pp. 305-314. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm169-3-6/