On Weak Tail Domination of Random Vectors

Volume 57 / 2009

Rafa/l Lata/la Bulletin Polish Acad. Sci. Math. 57 (2009), 75-80 MSC: Primary 60E15; Secondary 60G50, 52A40. DOI: 10.4064/ba57-1-8

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.

Authors

  • Rafa/l Lata/laInstitute of Mathematics
    Warsaw University
    Banacha 2
    02-097 Warszawa, Poland
    and
    Institute of Mathematics
    Polish Academy of Sciences
    Śniadeckich 8
    P.O. Box 21
    00-956 Warszawa 10, Poland
    e-mail

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