Asymptotic behaviour of averages of k-dimensional marginals of measures on ℝⁿ
Jesús Bastero ; Julio Bernués
Studia Mathematica, Tome 192 (2009), p. 1-31 / Harvested from The Polish Digital Mathematics Library
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We study the asymptotic behaviour, as n → ∞, of the Lebesgue measure of the set x∈K:|PE(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 ℝk of a t-dilate of the Euclidean unit ball. Some of the results hold for a wider class of probabilities on ℝⁿ.

Publié le : 2009-01-01
EUDML-ID : urn:eudml:doc:285088 
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Jesús Bastero; Julio Bernués. Asymptotic behaviour of averages of k-dimensional marginals of measures on ℝⁿ. Studia Mathematica, Tome 192 (2009) pp. 1-31. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm190-1-1/