两两独立Rademacher随机变量的Khinchine型不等式
On Khinchine type inequalities for pairwise independent Rademacher random variables
摘要：
研究$N$两两独立Rademacher随机变量向量的$p$阶矩的Khintchine型不等式.我们建立一个类似的欣钦不等式不能在这种设置与一个常数是独立的$N$ ;事实上，我们证明，最好的常数可以希望至少是$N^{1/2-1/p}$。此外，我们表明，这种估计是尖锐的交换向量时，$p = 4$。作为一个幸运的结果，我们的工作，我们得到了类似的结果$3$明智的独立向量。
英文摘要：
We consider Khintchine type inequalities on the $p$-th moments of vectors of $N$ pairwise independent Rademacher random variables. We establish that an analogue of Khintchine's inequality cannot hold in this setting with a constant that is independent of $N$; in fact, we prove that the best constant one can hope for is at least $N^{1/2-1/p}$. Furthermore, we show that this estimate is sharp for exchangeable vectors when $p = 4$. As a fortunate consequence of our work, we obtain similar results for $3$-wise independent vectors.
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