This is an announcement for the paper "On Khinchine type inequalities for pairwise independent Rademacher random variables" by Brendan Pass and Susanna Spektor.

Abstract: 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.

Archive classification: math.FA math.PR

Submitted from: sanaspek@yandex.ru

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1412.7859

or

http://arXiv.org/abs/1412.7859