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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.
Rafał Latała. "On Weak Tail Domination of Random Vectors." Bulletin of the Polish Academy of Sciences. Mathematics 57.1 (2009): 75-80. <http://eudml.org/doc/281200>.
@article{RafałLatała2009, abstract = {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.}, author = {Rafał Latała}, journal = {Bulletin of the Polish Academy of Sciences. Mathematics}, keywords = {sums of independent random variables; Bernoulli series; random vectors; log-concave distributions}, language = {eng}, number = {1}, pages = {75-80}, title = {On Weak Tail Domination of Random Vectors}, url = {http://eudml.org/doc/281200}, volume = {57}, year = {2009}, }
TY - JOUR AU - Rafał Latała TI - On Weak Tail Domination of Random Vectors JO - Bulletin of the Polish Academy of Sciences. Mathematics PY - 2009 VL - 57 IS - 1 SP - 75 EP - 80 AB - 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. LA - eng KW - sums of independent random variables; Bernoulli series; random vectors; log-concave distributions UR - http://eudml.org/doc/281200 ER -