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arXiv · 1306.6794

Thin-shell concentration for convex measures

Matthieu Fradelizi·Olivier Guédon·Alain Pajor
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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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Matthieu Fradelizi, Olivier Guédon, Alain Pajor. 2013-06-28. Thin-shell concentration for convex measures. https://arxiv.org/abs/1306.6794

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