Bounds on the concentration function in terms of Diophantine approximation
نویسندگان
چکیده
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 generalisa-tion. Des bornes pour la fonction de concentration enmatì ere d'approximation Diophantienne. Nous montrons un simple raison-nement analytique qui peutêtre 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 Rudel-son et Vershynin, et sa généralisation au cadre multidimensionel.
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