A+ CATEGORY SCIENTIFIC UNIT

Thin-shell concentration for convex measures

Volume 223 / 2014

Matthieu Fradelizi, Olivier Guédon, Alain Pajor Studia Mathematica 223 (2014), 123-148 MSC: Primary 60E15, 60F10, 52A23; Secondary 52A40, 46B09. DOI: 10.4064/sm223-2-2

Abstract

We prove that for $s<0$, $s$-concave measures on $\mathbb {R}^n$ exhibit thin-shell concentration similar to the log-concave case. This leads to a Berry–Esseen type estimate for most of their one-dimensional marginal distributions. We also establish sharp reverse Hölder inequalities for $s$-concave measures.

Authors

  • Matthieu FradeliziUniversité Paris-Est
    Laboratoire d'Analyse et Mathématiques Appliquées (UMR 8050)
    UPEMLV
    F-77454 Marne-la-Vallée Cedex 2, France
    e-mail
  • Olivier GuédonUniversité Paris-Est
    Laboratoire d'Analyse et Mathématiques Appliquées (UMR 8050)
    UPEMLV
    F-77454 Marne-la-Vallée Cedex 2, France
    e-mail
  • Alain PajorUniversité Paris-Est
    Laboratoire d'Analyse et Mathématiques Appliquées (UMR 8050)
    UPEMLV
    F-77454 Marne-la-Vallée Cedex 2, France
    e-mail

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