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Comptes Rendus Mathématique
Volume 346, n° 15-16
pages 853-856 (août 2008)
Doi : 10.1016/j.crma.2008.07.011
Received : 30 June 2008 ;  accepted : 10 July 2008
Smallest singular value of random matrices with independent columns
Sur la plus petite valeur singulière de matrices aléatoires avec des colonnes indépendantes
 

Radosław Adamczak a, 1 , Olivier Guédon b , Alexander Litvak c , Alain Pajor d , Nicole Tomczak-Jaegermann c, 2
a Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland 
b Université Pierre-et-Marie-Curie, Paris 6, Institut de mathématiques de Jussieu, 4, place Jussieu, 75005 Paris, France 
c Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1 
d Équipe dʼanalyse et mathématiques appliquées, Université Paris Est, 5, boulevard Descartes, Champs-sur-Marne, 77454 Marne-la-Vallee cedex 2, France 

Abstract

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. To cite this article: R. Adamczak et al., C. R. Acad. Sci. Paris, Ser. I 346 (2008).

The full text of this article is available in PDF format.
Résumé

On étudie la plus petite valeur singulière dʼune 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 dʼisotropie. Pour citer cet article : R. Adamczak et al., C. R. Acad. Sci. Paris, Ser. I 346 (2008).

The full text of this article is available in PDF format.
1  This work was done when this author held a postdoctoral position at the Department of Mathematical and Statistical Sciences, University of Alberta in Edmonton, Alberta. The position was co-sponsored by the Pacific Institute for the Mathematical Sciences.
2  This author holds the Canada Research Chair in Geometric Analysis.


© 2008  Published by Elsevier Masson SAS de la part de Académie des sciences.
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