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 the expectation of the supremum of “symmetric exponential” processes, compared to the Gaussian ones in the Chevet inequality. This is used to give a sharp upper estimate for a quantity that controls uniformly the Euclidean operator norm of the submatrices 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 also show that our Chevet type inequality does not extend to general isotropic log-concave random matrices.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm210-1-3,
author = {Rados\l aw Adamczak and Rafa\l\ Lata\l a and Alexander E. Litvak and Alain Pajor and Nicole Tomczak-Jaegermann},
title = {Chevet type inequality and norms of submatrices},
journal = {Studia Mathematica},
volume = {209},
year = {2012},
pages = {35-56},
zbl = {1253.60005},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm210-1-3}
}
Radosław Adamczak; Rafał Latała; Alexander E. Litvak; Alain Pajor; Nicole Tomczak-Jaegermann. Chevet type inequality and norms of submatrices. Studia Mathematica, Tome 209 (2012) pp. 35-56. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm210-1-3/