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

Abstract

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.

References in corpus (2)

• Tail estimates for norms of sums of log-concave random vectors
• Order statistics and concentration of l_r norms for log-concave vectors

Cited by in corpus (4)

• A short proof of Paouris' inequality
• Moment estimates for convex measures
• Tail estimates for norms of sums of log-concave random vectors
• Order statistics and concentration of l_r norms for log-concave vectors