A New Bound in the Littlewood–Offord Problem

Götze F, Zaitsev AY. A New Bound in the Littlewood–Offord Problem. Mathematics. 2022;10(10): 1740.The paper deals with studying a connection of the Littlewood–Offord problem with estimating the concentration functions of some symmetric infinitely divisible distributions. It is shown that the concentration function of a weighted sum of independent identically distributed random variables is estimated in terms of the concentration function of a symmetric infinitely divisible distribution whose spectral measure is concentrated on the set of plus-minus weights