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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A note on subgaussian estimates for linear functionals on convex bodies
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by A. Giannopoulos, A. Pajor and G. Paouris PDF
Proc. Amer. Math. Soc. 135 (2007), 2599-2606 Request permission

Abstract:

We give an alternative proof of a recent result of Klartag on the existence of almost subgaussian linear functionals on convex bodies. If $K$ is a convex body in ${\mathbb R}^n$ with volume one and center of mass at the origin, there exists $x\neq 0$ such that \[ |\{ y\in K: |\langle y,x\rangle |\geq t\|\langle \cdot ,x\rangle \|_1\}|\leq \exp (-ct^2/\log ^2(t+1))\] for all $t\geq 1$, where $c>0$ is an absolute constant. The proof is based on the study of the $L_q$–centroid bodies of $K$. Analogous results hold true for general log-concave measures.
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Additional Information
  • A. Giannopoulos
  • Affiliation: Department of Mathematics, University of Athens, Panepistimiopolis 157 84, Athens, Greece
  • Email: apgiannop@math.uoa.gr
  • A. Pajor
  • Affiliation: Équipe d’Analyse et de Mathématiques Appliquées, Université de Marne-la-Vallée, Champs sur Marne, 77454, Marne-la-Vallée, Cedex 2, France
  • Email: Alain.Pajor@univ-mlv.fr
  • G. Paouris
  • Affiliation: Équipe d’Analyse et de Mathématiques Appliquées, Université de Marne-la-Vallée, Champs sur Marne, 77454, Marne-la-Vallée, Cedex 2, France
  • MR Author ID: 671202
  • Email: grigoris_paouris@yahoo.co.uk
  • Received by editor(s): April 20, 2006
  • Published electronically: March 29, 2007
  • Additional Notes: The project was co-funded by the European Social Fund and National Resources - (EPEAEK II) “Pythagoras II". The second named author would like to thank the Department of Mathematics of the University of Athens for the hospitality. The third named author was supported by a Marie Curie Intra-European Fellowship (EIF), Contract MEIF-CT-2005-025017.
  • Communicated by: N. Tomczak-Jaegermann
  • © Copyright 2007 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 135 (2007), 2599-2606
  • MSC (2000): Primary 52A20; Secondary 46B07
  • DOI: https://doi.org/10.1090/S0002-9939-07-08778-3
  • MathSciNet review: 2302581