论文标题
Boppana-Holzman绑定到Rademacher随机变量的改进
An improvement of the Boppana-Holzman bound for Rademacher random variables
论文作者
论文摘要
令$ v_1，v_2，...，v_n $为实数，其正方形总计$ 1 $。考虑$ 2^n $签名的$ s = \ s = \ sum_ {i = 1}^n \ pm v_i。$ holzman and Kleitman（1992）证明，至少$ \ frac38 = 0.375 $ \ frac38 = 0.375 $中的这些和在$ | \ s的范围中，$ | \ s | \ s. $ for bound to bounts to in obles of $ s $ s $ s boppana（$ s boppana） $ \ frac {13} {32} = 0.40625 $，甚至更好到$ \ frac {13} {32} {32} +9 \ times10^{ - 6}。$遵循它们的方法，但是使用Bentkus和dzindzalieta（2015）的关键结果，您将比5 \ 5 \ 5 \ fy-5 \％。 $ \ frac {13} {32} $ to $ \ frac {1} {2} {2} - \ frac {φ（-2）} {4φ（ - \ sqrt {2}}} \ aid 0.42768。
Let $v_1,v_2,...,v_n$ be real numbers whose squares add up to $1$. Consider the $2^n$ signed sums of the form $S=\sum_{i=1}^n \pm v_i.$ Holzman and Kleitman (1992) proved that at least $\frac38=0.375$ of these sums satisfy $|S|\leq 1.$ By using bounds for appropriate moments of $S,$ Boppana and Holzman (2017) were able to improve the bound to $\frac{13}{32}=0.40625$ and even a bit better to $\frac{13}{32}+9\times10^{-6}.$ By following their approach, but using a key result of Bentkus and Dzindzalieta (2015), we will drastically improve (by more than 5\%) the latter barrier $\frac{13}{32}$ to $\frac{1}{2}-\frac{Φ(-2)}{4Φ(-\sqrt{2})}\approx 0.42768.$
