✦ LIBER ✦

Random Vectors in the Isotropic Position

✍ Scribed by M. Rudelson

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 123 KB
Volume: 164
Category: Article
ISSN: 0022-1236
DOI: 10.1006/jfan.1998.3384

No coin nor oath required. For personal study only.

✦ Synopsis

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 y i . We prove that for some absolute constant

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.

1999 Academic Press 1 vol (K) | K (x, y) 2 dy=&x& 2 .

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