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Thin-shell concentration for convex measures
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classification
math.FA
keywords
measuresconcaveconcentrationberry-esseenconvexdimensionaldistributionsestablish
abstract
We prove that for $s<0$, $s$-concave measures on ${\mathbb R}^n$ satisfy a thin shell concentration similar to the log-concave one. It leads to a Berry-Esseen type estimate for their one dimensional marginal distributions. We also establish sharp reverse H\"older inequalities for $s$-concave measures.
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