Uniform Uncertainty Principle for Bernoulli and Subgaussian Ensembles
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- Mendelson, S., Pajor, A. & Tomczak-Jaegermann, N. Constr Approx (2008) 28: 277. doi:10.1007/s00365-007-9005-8
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The paper considers random matrices with independent subgaussian columns and provides a new elementary proof of the Uniform Uncertainty Principle for such matrices. The Principle was introduced by Candes, Romberg and Tao in 2004; for subgaussian random matrices it was carlier proved by the present authors, as a consequence of a general result based on a generic chaining method of Talagrand. The present proof combines a simple measure concentration and a covering argument, which are standard tools of high-dimensional convexity.