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

Radosław Adamczak, Rafał Latała, Alexander E. Litvak, Alain Pajor, Nicole Tomczak-Jaegermann
2011 Comptes rendus. Mathematique  
We study the Restricted Isometry Property of a random matrix Γ with independent isotropic log-concave rows. To this end, we introduce a parameter Γ_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.
doi:10.1016/j.crma.2011.06.025 fatcat:6sl3cpb76bekjh3ay4xqz3fejm