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Journal of Mathematical Sciences

, Volume 206, Issue 2, pp 146–158 | Cite as

Estimates for the Concentration Functions in the Littlewood–Offord Problem

  • Yu. S. Eliseeva
  • F. Götze
  • A. Yu. Zaitsev
Article

Let X,X1, . . . , Xn be independent, identically distributed random variables. In this paper, we study the behavior of concentration functions of the weighted sums \( {\displaystyle \sum_{k=1}^n{a}_k{X}_k} \) with respect to the arithmetic structure of coefficients ak. Such concentration results recently became important in connection with the study of singular values of random matrices. In this paper, we formulate and prove some refinements of a result of Vershynin (2014).

Keywords

Characteristic Function Random Matrice Independent Random Variable Concentration Function Concentration Result 
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© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.St. Petersburg State UniversitySt. PetersburgRussia
  2. 2.Bielefeld UniversityBielefeldGermany
  3. 3.St. Petersburg Department of the Steklov Mathematical Institute and St. Petersburg State UniversitySt. PetersburgRussia

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