Small ball probability estimates in terms of width
Tom 169 / 2005
Studia Mathematica 169 (2005), 305-314
MSC: Primary 60G15; Secondary 60E15.
DOI: 10.4064/sm169-3-6
Streszczenie
A certain inequality conjectured by Vershynin is studied. It is proved that for any symmetric convex body 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.
