We discuss a method for obtaining Poincaré-type inequalities on arbitrary convex bodies in . Our technique involves a dual version of Bochner’s formula and a certain moment map, and it also applies to some non-convex sets. In particular, we generalize the central limit theorem for convex bodies to a class of non-convex domains, including the unit balls of -spaces in for .
Nous explorons un procédé de preuve d’inégalités de type Poincaré sur les corps convexes de . Notre technique utilise une version duale de la formule de Bochner et une application moment. Elle s’applique également à certains corps non-convexes. En particulier, nous généralisons le théorème central limite pour les ensembles convexes à une classe de domaines non-convexes, qui comprend les boules unités de munies de la norme pour .
@article{AFST_2013_6_22_1_1_0,
author = {Bo{\textquoteright}az Klartag},
title = {Poincar\'e {Inequalities} and {Moment} {Maps}},
journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
pages = {1--41},
publisher = {Universit\'e Paul Sabatier, Institut de Math\'ematiques},
address = {Toulouse},
volume = {Ser. 6, 22},
number = {1},
year = {2013},
doi = {10.5802/afst.1366},
zbl = {1279.60036},
language = {en},
url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1366/}
}
TY - JOUR AU - Bo’az Klartag TI - Poincaré Inequalities and Moment Maps JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2013 SP - 1 EP - 41 VL - 22 IS - 1 PB - Université Paul Sabatier, Institut de Mathématiques PP - Toulouse UR - https://afst.centre-mersenne.org/articles/10.5802/afst.1366/ DO - 10.5802/afst.1366 LA - en ID - AFST_2013_6_22_1_1_0 ER -
%0 Journal Article %A Bo’az Klartag %T Poincaré Inequalities and Moment Maps %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2013 %P 1-41 %V 22 %N 1 %I Université Paul Sabatier, Institut de Mathématiques %C Toulouse %U https://afst.centre-mersenne.org/articles/10.5802/afst.1366/ %R 10.5802/afst.1366 %G en %F AFST_2013_6_22_1_1_0
Bo’az Klartag. Poincaré Inequalities and Moment Maps. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 22 (2013) no. 1, pp. 1-41. doi : 10.5802/afst.1366. https://afst.centre-mersenne.org/articles/10.5802/afst.1366/
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