This is an announcement for the paper "Chevet type inequality and norms of submatrices" by Radoslaw Adamczak, Rafal Latala, Alexander E. Litvak, Alain Pajor, and Nicole Tomczak-Jaegermann.

Abstract: We prove a Chevet type inequality which gives an upper bound for the norm of an isotropic log-concave unconditional random matrix in terms of expectation of the supremum of ``symmetric exponential" processes compared to the Gaussian ones in the Chevet inequality. This is used to give sharp upper estimate for a quantity $\Gamma_{k,m}$ that controls uniformly the Euclidean operator norm of the sub-matrices with $k$ rows and $m$ columns of an isotropic log-concave unconditional random matrix. We apply these estimates to give a sharp bound for the Restricted Isometry Constant of a random matrix with independent log-concave unconditional rows. We show also that our Chevet type inequality does not extend to general isotropic log-concave random matrices.

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/1107.4066

or

http://arXiv.org/abs/1107.4066