On the Littlewood--Offord problem

Understand

The paper deals with studying a connection of the Littlewood--Offord problem with estimating the concentration functions of some symmetric infinitely divisible distributions.

• Some multivariate generalizations of results of Arak (1980) are given.
• They show a connection of the concentration function of the sum with the arithmetic structure of supports of distributions of independent random vectors for arbitrary distributions of summands.