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Random Vectors in the Isotropic Position
Open accessAbstract
Abstract Letybe a random vector in R n, satisfying E y⊗y=id. LetMbe a natural number and lety1, …, yMbe independent copies ofy. We study the question of approximation of the identity operator by finite sums of the tensorsyi⊗yi. We prove that for some absolute constantC E 1 M ∑ i=1 M y i ⊗y i −id ⩽C· log n M ·( E ‖y‖ log M ) 1/log M , 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.
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Metadata
- Authors
- Rudelson, M.
- Venue
- Journal of Functional Analysis
- Publisher
- Elsevier BV
- Published
- 1999-05
- Volume
- 164
- Issue
- 1
- Pages
- 60-72
- ISSN
- 0022-1236 (ISSN-L)
- OpenAlex
- W1967134148
- Cited by
- 371
- References
- 0
- FWCI
- 3.31
- Type
- journal article
- Language
- en
- Open access
- bronze
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- Rudelson, M. (1999). Random Vectors in the Isotropic Position. Journal of Functional Analysis. https://doi.org/10.1006/jfan.1998.3384
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