On some vector balancing problems

Giannopoulos, Apostolos

Studia Mathematica, Tome 122 (1997), p. 225-234 / Harvested from The Polish Digital Mathematics Library

Résumé

Let V be an origin-symmetric convex body in $ℝ^{n}$ , n≥ 2, of Gaussian measure $γ_{n} (V) \geq 1 / 2$ . It is proved that for every choice $u_{1}, . . ., u_{n}$ of vectors in the Euclidean unit ball $B_{n}$ , there exist signs $ε_{j} \in - 1, 1$ with $ε_{1} u_{1} + . . . + ε_{n} u_{n} \in (c l o g n) V$ . The method used can be modified to give simple proofs of several related results of J. Spencer and E. D. Gluskin.

Publié le : 1997-01-01
EUDML-ID : urn:eudml:doc:216373

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     author = {Apostolos Giannopoulos},
     title = {On some vector balancing problems},
     journal = {Studia Mathematica},
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     year = {1997},
     pages = {225-234},
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Giannopoulos, Apostolos. On some vector balancing problems. Studia Mathematica, Tome 122 (1997) pp. 225-234. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv122i3p225bwm/

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