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A reverse entropy power inequality for log-concave random vectors

Volume 235 / 2016

Keith Ball, Piotr Nayar, Tomasz Tkocz Studia Mathematica 235 (2016), 17-30 MSC: Primary 94A17; Secondary 52A40, 60E15. DOI: 10.4064/sm8418-6-2016 Published online: 23 September 2016

Abstract

We prove that the exponent of the entropy of one-dimensional projections of a log-concave random vector defines a $1/5$-seminorm. We make two conjectures concerning reverse entropy power inequalities in the log-concave setting and discuss some examples.

Authors

  • Keith BallMathematics Institute
    University of Warwick
    Coventry CV4 7AL, UK
    e-mail
  • Piotr NayarInstitute of Mathematics & Applications
    Minneapolis, MN 55455, U.S.A.
    e-mail
  • Tomasz TkoczMathematics Institute
    University of Warwick
    Coventry CV4 7AL, UK
    e-mail

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