Nous montrons un simple raisonnement analytique qui peut être utile pour borner la fonction de concentration d'une somme des variables aléatoires indépendantes. L'application principale est une version de l'inégalité récente de Rudelson et Vershynin, et sa généralisation au cadre multidimensionel.
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.
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@article{CRMATH_2007__345_9_513_0, author = {Friedland, Omer and Sodin, Sasha}, title = {Bounds on the concentration function in terms of the {Diophantine} approximation}, journal = {Comptes Rendus. Math\'ematique}, pages = {513--518}, publisher = {Elsevier}, volume = {345}, number = {9}, year = {2007}, doi = {10.1016/j.crma.2007.10.006}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2007.10.006/} }
TY - JOUR AU - Friedland, Omer AU - Sodin, Sasha TI - Bounds on the concentration function in terms of the Diophantine approximation JO - Comptes Rendus. Mathématique PY - 2007 SP - 513 EP - 518 VL - 345 IS - 9 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2007.10.006/ DO - 10.1016/j.crma.2007.10.006 LA - en ID - CRMATH_2007__345_9_513_0 ER -
%0 Journal Article %A Friedland, Omer %A Sodin, Sasha %T Bounds on the concentration function in terms of the Diophantine approximation %J Comptes Rendus. Mathématique %D 2007 %P 513-518 %V 345 %N 9 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2007.10.006/ %R 10.1016/j.crma.2007.10.006 %G en %F CRMATH_2007__345_9_513_0
Friedland, Omer; Sodin, Sasha. Bounds on the concentration function in terms of the Diophantine approximation. Comptes Rendus. Mathématique, Tome 345 (2007) no. 9, pp. 513-518. doi : 10.1016/j.crma.2007.10.006. http://archive.numdam.org/articles/10.1016/j.crma.2007.10.006/
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