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A note on subgaussian estimates for linear functionals on convex bodies

Authors:	A. Giannopoulos A. Pajor G. Paouris

Affiliation:	Department of Mathematics, University of Athens, Panepistimiopolis 157 84, Athens, Greece ; Équipe d'Analyse et de Mathématiques Appliquées, Université de Marne-la-Vallée, Champs sur Marne, 77454, Marne-la-Vallée, Cedex 2, France ; Équipe d'Analyse et de Mathématiques Appliquées, Université de Marne-la-Vallée, Champs sur Marne, 77454, Marne-la-Vallée, Cedex 2, France

Abstract:	We give an alternative proof of a recent result of Klartag on the existence of almost subgaussian linear functionals on convex bodies. If is a convex body in ${mathbb{R}}^n$ with volume one and center of mass at the origin, there exists such that $displaystyle vert{ yin K:,vertlangle y,xrangle vertgeq tVertlanglecdot ,xrangleVert _1}vertleqexp (-ct^2/log^2(t+1))$ for all , where is an absolute constant. The proof is based on the study of the -centroid bodies of . Analogous results hold true for general log-concave measures.

Keywords:	Isotropic convex bodies concentration of volume tail estimates for linear functionals $L_q$--centroid bodies

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