Geometry of log-concave Ensembles of random matrices and approximate   reconstruction
  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. 
Rados{\l}aw Adamczak, Rafa{\l} Lata{\l}a, Alexander E. Litvak, Alain   Pajor, Nicole Tomczak-Jaegermann
math.PR math.FA math.MG