Thin-shell concentration for convex measures
Volume 223 / 2014
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.
