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A note on subgaussian estimates for linear functionals on convex bodies |
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| 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  with volume one and center of mass at the origin, there exists  such that   , 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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