A pr 2 00 6 L p moments of random vectors via majorizing measures

  title={A pr 2 00 6 L p moments of random vectors via majorizing measures},
  author={Olivier Gu{\'e}don and Mark Rudelson},
For a random vector X in Rn, we obtain bounds on the size of a sample, for which the empirical p-th moments of linear functionals are close to the exact ones uniformly on a convex bodyK ⊂ Rn. We prove an estimate for a general random vector and apply it to several problems arising in geometric functional analysis. In particular, we find a short Lewis type decomposition for any finite dimensional subspace of Lp. We also prove that for an isotropic log-concave random vector, we only need ⌊np/2… CONTINUE READING
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