Functional Analysis
Smallest singular value of random matrices with independent columns
[Sur la plus petite valeur singulière de matrices aléatoires avec des colonnes indépendantes]
Comptes Rendus. Mathématique, Tome 346 (2008) no. 15-16, pp. 853-856.

On étudie la plus petite valeur singulière d'une matrice carrée aléatoire dont les colonnes sont des vecteurs aléatoires i.i.d. suivant une loi à densité log-concave isotrope. On démontre une inégalité de déviation en fonction de la constante d'isotropie.

We study the smallest singular value of a square random matrix with i.i.d. columns drawn from an isotropic symmetric log-concave distribution. We prove a deviation inequality in terms of the isotropic constant of the distribution.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2008.07.011
Adamczak, Radosław 1 ; Guédon, Olivier 2 ; Litvak, Alexander 3 ; Pajor, Alain 4 ; Tomczak-Jaegermann, Nicole 3

1 Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland
2 Université Pierre-et-Marie-Curie, Paris 6, Institut de mathématiques de Jussieu, 4, place Jussieu, 75005 Paris, France
3 Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1
4 Équipe d'analyse et mathématiques appliquées, Université Paris Est, 5, boulevard Descartes, Champs-sur-Marne, 77454 Marne-la-Vallee cedex 2, France
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     author = {Adamczak, Rados{\l}aw and Gu\'edon, Olivier and Litvak, Alexander and Pajor, Alain and Tomczak-Jaegermann, Nicole},
     title = {Smallest singular value of random matrices with independent columns},
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Adamczak, Radosław; Guédon, Olivier; Litvak, Alexander; Pajor, Alain; Tomczak-Jaegermann, Nicole. Smallest singular value of random matrices with independent columns. Comptes Rendus. Mathématique, Tome 346 (2008) no. 15-16, pp. 853-856. doi : 10.1016/j.crma.2008.07.011. http://www.numdam.org/articles/10.1016/j.crma.2008.07.011/

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