  Consider a sum $S_n=v_i\varepsilon_1+\cdots+v_n\varepsilon_{n}$, where
$(v_i)^{n}_{i=1}$ are non-zero vectors in $\mathbb{R}^{d}$ and
$(\varepsilon_i)^{n}_{i=1}$ are independent Rademacher random variables (i.e.,
$~{\mathbb{P}(\varepsilon_{i}=\pm 1)=1/2}$). The classical Littlewood-Offord
problem asks for the best possible upper bound for $~{\sup_{x}\mathbb{P}(S_n =
x)}$. In this paper we consider a non-uniform version of this problem. Namely,
we obtain the optimal bound for $\mathbb{P}(S_n = x)$ in terms of the length of
the vector $x\in \mathbb{R}^d$.
