Abstract
Consider a sum Sn=viε1+⋯+vnεn, where (vi)i=1n are non-zero vectors in Rd and (εi)i=1n are independent Rademacher random variables (i.e., P(εi=±1)=12). The classical Littlewood–Offord problem asks for the best possible upper bound for supxP(Sn=x). In this paper we consider a non-uniform version of this problem. Namely, we obtain the optimal bound for P(Sn=x) in terms of the length of the vector x∈Rd.
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