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

• Autorzy: Jesús Bastero , Julio Bernués
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 60F05: Central limit and other weak theorems
• 53A20: Projective differential geometry

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2009
• Tom: 190
• Numer: 1
• Strony: 1-31

Daty

wydano

2009

Twórcy

autor

Jesús Bastero

• Departamento de Matemáticas, Universidad de Zaragoza, 50009 Zaragoza, Spain

autor

Julio Bernués

• Departamento de Matemáticas, Universidad de Zaragoza, 50009 Zaragoza, Spain

Identyfikatory

DOI

10.4064/sm190-1-1