Chevet type inequality and norms of submatrices

Radosław Adamczak, et al. "Chevet type inequality and norms of submatrices." Studia Mathematica 210.1 (2012): 35-56. <http://eudml.org/doc/285432>.

@article{RadosławAdamczak2012,
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 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 $Γ_\{k,m\}$ 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.},
author = {Radosław Adamczak, Rafał Latała, Alexander E. Litvak, Alain Pajor, Nicole Tomczak-Jaegermann},
journal = {Studia Mathematica},
keywords = {log-concave random vectors; concentration inequalities; deviation inequalities; random matrices; restricted isometry property; Chevet inequality},
language = {eng},
number = {1},
pages = {35-56},
title = {Chevet type inequality and norms of submatrices},
url = {http://eudml.org/doc/285432},
volume = {210},
year = {2012},
}

TY - JOUR
AU - Radosław Adamczak
AU - Rafał Latała
AU - Alexander E. Litvak
AU - Alain Pajor
AU - Nicole Tomczak-Jaegermann
TI - Chevet type inequality and norms of submatrices
JO - Studia Mathematica
PY - 2012
VL - 210
IS - 1
SP - 35
EP - 56
AB - 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 $Γ_{k,m}$ 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.
LA - eng
KW - log-concave random vectors; concentration inequalities; deviation inequalities; random matrices; restricted isometry property; Chevet inequality
UR - http://eudml.org/doc/285432
ER -