Approximating the moments of marginals of high dimensional distributions

Details Approximating the moments of marginals of high dimensional distributions Approximating the moments of marginals of high dimensional distributions

2009-11-02

arxiv.org/abs/0911.0391v3

Mathematics

Probability

16 pages. A few minor inaccuracies corrected in the argument

Scientific paper

For probability distributions on R^n, we study the optimal sample size N=N(n,p) that suffices to uniformly approximate the p-th moments of all one-dimensional marginals. Under the assumption that the marginals have bounded 4p moments, we obtain the optimal bound N = O(n^{p/2}) for p > 2. This bound goes in the direction of bridging the two recent results: a theorem of Guedon and Rudelson which has an extra logarithmic factor in the sample size, and a recent result of Adamczak, Litvak, Pajor and Tomczak-Jaegermann which requires stronger subexponential moment assumptions.

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