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A note on subgaussian estimates for linear functionals on convex bodies

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 R-n with volume one and center of mass at the origin, there exists x not equal 0 such that vertical bar{y is an element of K : vertical bar y, x vertical bar >= t vertical bar vertical bar ., x vertical bar vertical bar 1} vertical bar <= exp(-ct(2) / log(2) (t+1)) for all t = 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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https://hal-upec-upem.archives-ouvertes.fr/hal-00693704
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Submitted on : Wednesday, May 2, 2012 - 10:43:42 PM
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A. Giannopoulos, Alain Pajor, G. Paouris. A note on subgaussian estimates for linear functionals on convex bodies. Proceedings of the American Mathematical Society, American Mathematical Society, 2007, 135 (8), pp.2599--2606. ⟨10.1090/S0002-9939-07-08778-3⟩. ⟨hal-00693704⟩

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