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 R n satisfy a thinshell concentration similar to the log-concave case. It 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 fatcat:7ejfwv7lrnafpmyyzviwsxv4zy