Small ball probability estimates in terms of width

Rafał Latała, and Krzysztof Oleszkiewicz. "Small ball probability estimates in terms of width." Studia Mathematica 169.3 (2005): 305-314. <http://eudml.org/doc/285251>.

@article{RafałLatała2005,
abstract = {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 $γₙ(sK) ≤ (2s)^\{w²/4\}γₙ(K)$ 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.},
author = {Rafał Latała, Krzysztof Oleszkiewicz},
journal = {Studia Mathematica},
language = {eng},
number = {3},
pages = {305-314},
title = {Small ball probability estimates in terms of width},
url = {http://eudml.org/doc/285251},
volume = {169},
year = {2005},
}

TY - JOUR
AU - Rafał Latała
AU - Krzysztof Oleszkiewicz
TI - Small ball probability estimates in terms of width
JO - Studia Mathematica
PY - 2005
VL - 169
IS - 3
SP - 305
EP - 314
AB - 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 $γₙ(sK) ≤ (2s)^{w²/4}γₙ(K)$ 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.
LA - eng
UR - http://eudml.org/doc/285251
ER -