Geodesic
Thin-shell concentration for convex measures
Matthieu Fradelizi 1   ; Olivier Guédon 1   ; Alain Pajor 1
1 Université Paris-Est Laboratoire d'Analyse et Mathématiques Appliquées (UMR 8050) UPEMLV F-77454 Marne-la-Vallée Cedex 2, France
Studia Mathematica, Tome 223 (2014) no. 2, pp. 123-148 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We prove that for $s0$, $s$-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.
DOI : 10.4064/sm223-2-2
Keywords: prove s concave measures mathbb exhibit thin shell concentration similar log concave leads berry esseen type estimate their one dimensional marginal distributions establish sharp reverse lder inequalities s concave measures

Matthieu Fradelizi  1   ; Olivier Guédon  1   ; Alain Pajor  1

1 Université Paris-Est Laboratoire d'Analyse et Mathématiques Appliquées (UMR 8050) UPEMLV F-77454 Marne-la-Vallée Cedex 2, France 
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Matthieu Fradelizi; Olivier Guédon; Alain Pajor. Thin-shell concentration for convex measures. Studia Mathematica, Tome 223 (2014) no. 2, pp. 123-148. doi: 10.4064/sm223-2-2

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