Randomizing properties of convex high-dimensional bodies and some geometric inequalities
Comptes Rendus. Mathématique, Volume 334 (2002) no. 10, pp. 875-879.

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”.

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 ».

Received:
Accepted:
DOI: 10.1016/S1631-073X(02)02350-6
Gluskin, Efim 1; Milman, Vitali 1

1 School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel
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Gluskin, Efim; Milman, Vitali. Randomizing properties of convex high-dimensional bodies and some geometric inequalities. Comptes Rendus. Mathématique, Volume 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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