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Comptes Rendus Mathématique
Volume 345, n° 9
pages 513-518 (novembre 2007)
Doi : 10.1016/j.crma.2007.10.006
Received : 14 August 2007 ;  accepted : 28 September 2007
Bounds on the concentration function in terms of the Diophantine approximation
Des bornes pour la fonction de concentration en matière dʼapproximation diophantienne
 

Omer Friedland , Sasha Sodin
School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel 

Abstract

We demonstrate a simple analytic argument that may be used to bound the Lévy concentration function of a sum of independent random variables. The main application is a version of a recent inequality due to Rudelson and Vershynin, and its multidimensional generalization. To cite this article: O. Friedland, S. Sodin, C. R. Acad. Sci. Paris, Ser. I 345 (2007).

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

Nous montrons un simple raisonnement analytique qui peut être utile pour borner la fonction de concentration dʼune somme des variables aléatoires indépendantes. Lʼapplication principale est une version de lʼinégalité récente de Rudelson et Vershynin, et sa généralisation au cadre multidimensionel. Pour citer cet article : O. Friedland, S. Sodin, C. R. Acad. Sci. Paris, Ser. I 345 (2007).

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


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