Thin-shell concentration for convex measures

Matthieu Fradelizi, Olivier Guédon, and Alain Pajor. "Thin-shell concentration for convex measures." Studia Mathematica 223.2 (2014): 123-148. <http://eudml.org/doc/285659>.

@article{MatthieuFradelizi2014,
abstract = {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.},
author = {Matthieu Fradelizi, Olivier Guédon, Alain Pajor},
journal = {Studia Mathematica},
keywords = {isotropic; convex measure; concentration inequalities; thin-shell; large-deviation; KLS conjecture},
language = {eng},
number = {2},
pages = {123-148},
title = {Thin-shell concentration for convex measures},
url = {http://eudml.org/doc/285659},
volume = {223},
year = {2014},
}

TY - JOUR
AU - Matthieu Fradelizi
AU - Olivier Guédon
AU - Alain Pajor
TI - Thin-shell concentration for convex measures
JO - Studia Mathematica
PY - 2014
VL - 223
IS - 2
SP - 123
EP - 148
AB - 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.
LA - eng
KW - isotropic; convex measure; concentration inequalities; thin-shell; large-deviation; KLS conjecture
UR - http://eudml.org/doc/285659
ER -