Motivated by a question of Krzysztof Oleszkiewicz we study a notion of weak tail domination of random vectors. We show that if the dominating random variable is sufficiently regular then weak tail domination implies strong tail domination. In particular, a positive answer to Oleszkiewicz's question would follow from the so-called Bernoulli conjecture. We also prove that any unconditional logarithmically concave distribution is strongly dominated by a product symmetric exponential measure.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba57-1-8,
author = {Rafa\l\ Lata\l a},
title = {On Weak Tail Domination of Random Vectors},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {57},
year = {2009},
pages = {75-80},
zbl = {1170.60309},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba57-1-8}
}
Rafał Latała. On Weak Tail Domination of Random Vectors. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 57 (2009) pp. 75-80. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba57-1-8/