Chevet type inequality and norms of submatrices
Studia Mathematica, Tome 210 (2012) no. 1, pp. 35-56
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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
${\Gamma }_{k,m}$ 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.
Keywords:
prove chevet type inequality which gives upper bound norm isotropic log concave unconditional random matrix terms expectation supremum symmetric exponential processes compared gaussian chevet inequality sharp upper estimate quantity gamma controls uniformly euclidean operator norm submatrices rows columns isotropic log concave unconditional random matrix apply these estimates sharp bound restricted isometry constant random matrix independent log concave unconditional rows chevet type inequality does extend general isotropic log concave random matrices
Affiliations des auteurs :
Radosław Adamczak 1 ; Rafał Latała 2 ; Alexander E. Litvak 3 ; Alain Pajor 4 ; Nicole Tomczak-Jaegermann 3
@article{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},
pages = {35--56},
publisher = {mathdoc},
volume = {210},
number = {1},
year = {2012},
doi = {10.4064/sm210-1-3},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm210-1-3/}
}
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 SP - 35 EP - 56 VL - 210 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/sm210-1-3/ DO - 10.4064/sm210-1-3 LA - en ID - 10_4064_sm210_1_3 ER -
%0 Journal Article %A Radosław Adamczak %A Rafał Latała %A Alexander E. Litvak %A Alain Pajor %A Nicole Tomczak-Jaegermann %T Chevet type inequality and norms of submatrices %J Studia Mathematica %D 2012 %P 35-56 %V 210 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/sm210-1-3/ %R 10.4064/sm210-1-3 %G en %F 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 210 (2012) no. 1, pp. 35-56. doi: 10.4064/sm210-1-3
Cité par Sources :