The Littlewood-Offord problem in high dimensions and a conjecture of Frankl and Füredi

Details The Littlewood-Offord problem in high dimensions and a conjecture of Frankl and Füredi The Littlewood-Offord problem in high dimensions and a conjecture of Frankl and Füredi

2010-02-26

arxiv.org/abs/1002.5028v2

Mathematics

Combinatorics

8 pages, no figures. To appear, Combinatorica. This is the final version, incorporating the referee suggestions

Scientific paper

We give a new bound on the probability that the random sum $\xi_1 v_1 +...+ \xi_n v_n$ belongs to a ball of fixed radius, where the $\xi_i$ are iid Bernoulli random variables and the $v_i$ are vectors in $\R^d$. As an application, we prove a conjecture of Frankl and F\"uredi (raised in 1988), which can be seen as the high dimensional version of the classical Littlewood-Offord-Erd\H os theorem.

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