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Random vectors in the isotropic position
被引:0
|作者:
Rudelson, H
[1
]
机构:
[1] Univ Missouri, Dept Math, Columbia, MO 65211 USA
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D O I:
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中图分类号:
O1 [数学];
学科分类号:
0701 ;
070101 ;
摘要:
Let M be a natural number and let y(1),...,y(M) be independent copies of y. We study the question of approximation of the identity operator by finite sums of the tensors y(i) x y(i) We prove that for some absolute constant C E1/M Sigma(i=1)(M) y(i) x y(i)-id less than or equal to C. root logn/root M. (Ey(logM))(1/logM) provided that the last expression is smaller than 1. We apply this estimate to improve a result of Bourgain concerning the number of random points needed to bring a convex body into a nearly isotropic position. (C) 1999 Academic Press.
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页码:60 / 72
页数:13
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