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Moment estimates for convex measures

Abstract : Let p ≥ 1, ε > 0, r ≥ (1+ε)p, and X be a (−1/r)-concave random vector in Rn with Euclidean norm |X|. We prove that where (E|X|p)1/p ≤c(C(ε)E|X|+σp(X)), σp(X)= sup(E|⟨z,X⟩|p)1/p, |z|≤1 C(ε) depends only on ε and c is a universal constant. Moreover, if in addition X is centered then (E|X|−p)−1/p ≥c(ε)(E|X|−Cσp(X)).
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Submitted on : Friday, February 22, 2013 - 11:39:31 PM
Last modification on : Tuesday, October 19, 2021 - 4:07:09 PM

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  • HAL Id : hal-00793780, version 1

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Radosław Adamczak, Olivier Guédon, Rafal Latala, Alexander Litvak, Krzysztof Oleszkiewicz, et al.. Moment estimates for convex measures. Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2012, 17, pp.101: 1-19. ⟨hal-00793780⟩

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