Mendelson, ShaharPajor, AlainTomczak-Jaegermann, Nicole2015-12-080176-4276http://hdl.handle.net/1885/31228The 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.Keywords: Approximate reconstruction; Generic chaining; Random matrices; Uniform uncertainty principleUniform Uncertainty Principle for Bernoulli and Subgaussian Ensembles200810.1007/s00365-007-9005-82016-02-24