Estimates for the concentration functions in the Littlewood--Offord problem

Details Estimates for the concentration functions in the Littlewood--Offord problem Estimates for the concentration functions in the Littlewood--Offord problem

2012-03-30

arxiv.org/abs/1203.6763v1

Mathematics

Probability

14 pages

Scientific paper

Let $X,X_1,...,X_n$ be independent identically distributed random variables. In this paper we study the behavior of the concentration functions of the weighted sums $\sum_{k=1}^{n}a_k X_k$ with respect to the arithmetic structure of coefficients $a_k$. Such concentration results recently became important in connection with investigations about singular values of random matrices. In this paper we formulate and prove some refinements of a result of Vershynin (2011).

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