This is an announcement for the paper "Approximating the moments of marginals of high dimensional distributions" by Roman Vershynin.
Abstract: 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 support of the distribution lies in the Euclidean ball of radius \sqrt{n} and 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.
Archive classification: math.PR math.FA
Mathematics Subject Classification: 46B09; 52A21; 62J10
Remarks: 12 pages
The source file(s), moments-of-marginals.tex: 32410 bytes, is(are) stored in gzipped form as 0911.0391.gz with size 11kb. The corresponding postcript file has gzipped size 92kb.
Submitted from: romanv@umich.edu
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