Abstract
Let $X,X_1,\ldots,X_n$ be independent identically distributed random variables. In this paper we study the behavior of concentration functions of weighted sums $\sum_{k=1}^{n}X_ka_k $ with respect to the arithmetic structure of coefficients $a_k$ in the context of the Littlewood--Offord problem. In recent papers of Eliseeva, G\"otze and Zaitsev, we discussed the relations between the inverse principles stated by Nguyen, Tao and Vu and similar principles formulated by Arak in his papers from the 1980's. In this paper, we will derive some more general and more precise consequences of Arak's inequalities providing new results in the context of the Littlewood-Offord problem.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have