Geometry of log-concave Ensembles of random matrices and approximate reconstruction

Details Geometry of log-concave Ensembles of random matrices and approximate reconstruction Geometry of log-concave Ensembles of random matrices and approximate reconstruction

2011-03-02

arxiv.org/abs/1103.0401v1

Mathematics

Probability

Scientific paper

We study the Restricted Isometry Property of a random matrix $\Gamma$ with independent isotropic log-concave rows. To this end, we introduce a parameter $\Gamma_{k,m}$ that controls uniformly the operator norm of sub-matrices with $k$ rows and $m$ columns. This parameter is estimated by means of new tail estimates of order statistics and deviation inequalities for norms of projections of an isotropic log-concave vector.

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