[Les propriétés aléatoires des corps convexes de grande dimension et une inégalité géométrique]
Nous étudions les propriétés des corps convexes liées à la distribution uniforme. En particulier, nous démontrons une borne inférieure pour la norme d'une somme de vecteurs aléatoires distribués géometriquement. Cette borne généralise le cas des vecteurs ayant la même distribution déjà étudié par Bourgain, Meyer, Milman et Pajor, et résout un problème posé par eux. Un autre corollaire énonce que chaque espace normé de dimension finie est de « cotype 2 aléatoire ».
Properties of convex bodies related to uniform distribution are studied. In particular, a low bound for the norm of the sum of independent geometrically distributed vectors is obtained. It extends the previously studied case of identically distributed vectors by Bourgain, Meyer, Milman and Pajor and solves a problem raised there. Another corollary asserts that any finite dimensional normed space has a “random cotype 2”.
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@article{CRMATH_2002__334_10_875_0,
author = {Gluskin, Efim and Milman, Vitali},
title = {Randomizing properties of convex high-dimensional bodies and some geometric inequalities},
journal = {Comptes Rendus. Math\'ematique},
pages = {875--879},
publisher = {Elsevier},
volume = {334},
number = {10},
year = {2002},
doi = {10.1016/S1631-073X(02)02350-6},
language = {en},
url = {http://www.numdam.org/articles/10.1016/S1631-073X(02)02350-6/}
}
TY - JOUR AU - Gluskin, Efim AU - Milman, Vitali TI - Randomizing properties of convex high-dimensional bodies and some geometric inequalities JO - Comptes Rendus. Mathématique PY - 2002 SP - 875 EP - 879 VL - 334 IS - 10 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/S1631-073X(02)02350-6/ DO - 10.1016/S1631-073X(02)02350-6 LA - en ID - CRMATH_2002__334_10_875_0 ER -
%0 Journal Article %A Gluskin, Efim %A Milman, Vitali %T Randomizing properties of convex high-dimensional bodies and some geometric inequalities %J Comptes Rendus. Mathématique %D 2002 %P 875-879 %V 334 %N 10 %I Elsevier %U http://www.numdam.org/articles/10.1016/S1631-073X(02)02350-6/ %R 10.1016/S1631-073X(02)02350-6 %G en %F CRMATH_2002__334_10_875_0
Gluskin, Efim; Milman, Vitali. Randomizing properties of convex high-dimensional bodies and some geometric inequalities. Comptes Rendus. Mathématique, Tome 334 (2002) no. 10, pp. 875-879. doi : 10.1016/S1631-073X(02)02350-6. http://www.numdam.org/articles/10.1016/S1631-073X(02)02350-6/
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