The optimal order for the p-th moment of sums of independent random variables with respect to symmetric norms and related combinatorial estimates

Details The optimal order for the p-th moment of sums of independent random variables with respect to symmetric norms and related combinatorial estimates The optimal order for the p-th moment of sums of independent random variables with respect to symmetric norms and related combinatorial estimates

2002-09-20

arxiv.org/abs/math/0209278v2

Mathematics

Probability

Scientific paper

We calculate the p-the moment of the sum of n independent random variables with respect to symmetric norm in R^n. The order of growth for upper bound p/ln p obtained in ths estimate is optimal. The result extends to generalized Lorentz spaces l_{f,w} under mild assumptions on f. Indeed, the key combinatorial estimate is obtained for the weak l_1 (l_{1,infinity})-norm. Similar results have been obtained independently by Gordon, Litvak, Schuett and Werner for Orlicz norms and by Montgomery-Smith using different techniques and avoiding the combinatorial estimate.

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