Abstract of a paper by Brendan Pass and Susanna Spektor
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
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alspach@math.okstate.edu