Asymptotic behaviour of averages of k-dimensional marginals of measures on ℝⁿ

Jesús Bastero, and Julio Bernués. "Asymptotic behaviour of averages of k-dimensional marginals of measures on ℝⁿ." Studia Mathematica 190.1 (2009): 1-31. <http://eudml.org/doc/285088>.

@article{JesúsBastero2009,
abstract = {We study the asymptotic behaviour, as n → ∞, of the Lebesgue measure of the set $\{x ∈ K: | P_E(x)| ≤ t\}$ for a random k-dimensional subspace E ⊂ ℝⁿ and an isotropic convex body K ⊂ ℝⁿ. For k growing slowly to infinity, we prove it to be close to the suitably normalised Gaussian measure in $ℝ^\{k\}$ of a t-dilate of the Euclidean unit ball. Some of the results hold for a wider class of probabilities on ℝⁿ.},
author = {Jesús Bastero, Julio Bernués},
journal = {Studia Mathematica},
keywords = {isotropic bodies; central limit; concentration phenomena},
language = {eng},
number = {1},
pages = {1-31},
title = {Asymptotic behaviour of averages of k-dimensional marginals of measures on ℝⁿ},
url = {http://eudml.org/doc/285088},
volume = {190},
year = {2009},
}

TY - JOUR
AU - Jesús Bastero
AU - Julio Bernués
TI - Asymptotic behaviour of averages of k-dimensional marginals of measures on ℝⁿ
JO - Studia Mathematica
PY - 2009
VL - 190
IS - 1
SP - 1
EP - 31
AB - We study the asymptotic behaviour, as n → ∞, of the Lebesgue measure of the set ${x ∈ K: | P_E(x)| ≤ t}$ for a random k-dimensional subspace E ⊂ ℝⁿ and an isotropic convex body K ⊂ ℝⁿ. For k growing slowly to infinity, we prove it to be close to the suitably normalised Gaussian measure in $ℝ^{k}$ of a t-dilate of the Euclidean unit ball. Some of the results hold for a wider class of probabilities on ℝⁿ.
LA - eng
KW - isotropic bodies; central limit; concentration phenomena
UR - http://eudml.org/doc/285088
ER -