论文标题
Tomaszewski在随机签名的总和上的猜想证明
Proof of Tomaszewski's Conjecture on Randomly Signed Sums
论文作者
论文摘要
由于Tomaszewski（1986），我们证明了以下猜想：令$ x = \ sum_ {i = 1}^{n} a_ {i} x_ {i} x_ {i} $，其中$ \ sum_i a_i a_i^2 = 1 $ and $ x_i $，每个$ x_i $都是均匀的随机符号。然后$ \ pr [| x | \ leq 1] \ geq 1/2 $。我们的主要新工具是局部浓度不平等和Rademacher总和改善的浆果 - Esseen不平等。
We prove the following conjecture, due to Tomaszewski (1986): Let $X= \sum_{i=1}^{n} a_{i} x_{i}$, where $\sum_i a_i^2=1$ and each $x_i$ is a uniformly random sign. Then $\Pr[|X|\leq 1] \geq 1/2$. Our main novel tools are local concentration inequalities and an improved Berry-Esseen inequality for Rademacher sums.
