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Thin-shell concentration for convex measures

Matthieu Fradelizi, Olivier Guédon, Alain Pajor (2014)

Studia Mathematica

We prove that for s < 0, s-concave measures on ℝⁿ 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.

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