[Géométrie des ensembles log-concave des matrices aléatoires et une reconstruction approximative]
On étudie la propriété dʼisométrie restreinte dʼune matrice aléatoire Γ dont les lignes sont des vecteurs aléatoires indépendants isotropes log-concave. Pour cela on introduit un paramètre qui contrôle uniformément les normes dʼopérateurs des sous-matrices de k lignes et m colonnes. Ce paramètre est estimé à lʼaide de nouvelles inégalités de queue des statistiques dʼordre et dʼinégalités de déviation des normes de projections dʼun vecteur aléatoire log-concave.
We study the Restricted Isometry Property of a random matrix Γ with independent isotropic log-concave rows. To this end, we introduce a parameter 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.
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@article{CRMATH_2011__349_13-14_783_0,
author = {Adamczak, Rados{\l}aw and Lata{\l}a, Rafa{\l} and Litvak, Alexander E. and Pajor, Alain and Tomczak-Jaegermann, Nicole},
title = {Geometry of log-concave ensembles of random matrices and approximate reconstruction},
journal = {Comptes Rendus. Math\'ematique},
pages = {783--786},
publisher = {Elsevier},
volume = {349},
number = {13-14},
year = {2011},
doi = {10.1016/j.crma.2011.06.025},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2011.06.025/}
}
TY - JOUR AU - Adamczak, Radosław AU - Latała, Rafał AU - Litvak, Alexander E. AU - Pajor, Alain AU - Tomczak-Jaegermann, Nicole TI - Geometry of log-concave ensembles of random matrices and approximate reconstruction JO - Comptes Rendus. Mathématique PY - 2011 SP - 783 EP - 786 VL - 349 IS - 13-14 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2011.06.025/ DO - 10.1016/j.crma.2011.06.025 LA - en ID - CRMATH_2011__349_13-14_783_0 ER -
%0 Journal Article %A Adamczak, Radosław %A Latała, Rafał %A Litvak, Alexander E. %A Pajor, Alain %A Tomczak-Jaegermann, Nicole %T Geometry of log-concave ensembles of random matrices and approximate reconstruction %J Comptes Rendus. Mathématique %D 2011 %P 783-786 %V 349 %N 13-14 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2011.06.025/ %R 10.1016/j.crma.2011.06.025 %G en %F CRMATH_2011__349_13-14_783_0
Adamczak, Radosław; Latała, Rafał; Litvak, Alexander E.; Pajor, Alain; Tomczak-Jaegermann, Nicole. Geometry of log-concave ensembles of random matrices and approximate reconstruction. Comptes Rendus. Mathématique, Tome 349 (2011) no. 13-14, pp. 783-786. doi : 10.1016/j.crma.2011.06.025. http://www.numdam.org/articles/10.1016/j.crma.2011.06.025/
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