高维Littlewood-Offord问题与Frankl和Füredi的一个猜想
The Littlewood-Offord problem in high dimensions and a conjecture of Frankl and Füredi
摘要：
本文给出了随机和$ξ_1 v_1 +...+ ξ_n v_n$属于固定半径球的概率的一个新的界，其中$ξ_i$是iid Bernoulli随机变量，$v_i$是$\R^d$中的向量.作为应用，我们证明了Frankl和Füredi在1988年提出的一个猜想，它可以看作是经典Littlewood-Offord-Erd \H os定理的高维版本.
英文摘要：
We give a new bound on the probability that the random sum $ξ_1 v_1 +...+ ξ_n v_n$ belongs to a ball of fixed radius, where the $ξ_i$ are iid Bernoulli random variables and the $v_i$ are vectors in $\R^d$. As an application, we prove a conjecture of Frankl and Füredi (raised in 1988), which can be seen as the high dimensional version of the classical Littlewood-Offord-Erd\H os theorem.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
