On the Littlewood--Offord problem
  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. 
Yulia S. Eliseeva, Andrei Yu. Zaitsev
math.PR