APPROXIMATING THE MOMENTS OF MARGINALS OF HIGH-DIMENSIONAL DISTRIBUTIONS

• 成果类型: Article
• 署名作者: Vershynin, Roman
• 署名单位: University of Michigan System; University of Michigan
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/10-AOP589
• 发表日期: 2011
• 页码: 1591-1606
• 关键词: matrix

摘要

For probability distributions on R-n, we study the optimal sample size N = N(n, p) that suffices to uniformly approximate the pth 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 [Adv. Math. 208 (2007) 798-823] which has an extra logarithmic factor in the sample size, and a result of Adamczak et al. [J. Amer. Math. Soc. 23 (2010) 535-561] which requires stronger subexponential moment assumptions.