This is an announcement for the paper "Geometry of log-concave ensembles of random matrices and approximate reconstruction" by Radoslaw Adamczak, Rafal Latala, Alexander E. Litvak, Alain Pajor, and Nicole Tomczak-Jaegermann.

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.

Archive classification: math.PR math.FA math.MG

Mathematics Subject Classification: Primary 52A23, 46B06, 46B09, 60E15 Secondary 15B52, 94B75

Submitted from: radamcz@mimuw.edu.pl

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1103.0401

or

http://arXiv.org/abs/1103.0401