A note on subgaussian estimates for linear functionals on convex bodies
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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 n with volume one and center of mass at the origin, there exists x 0 such that |{y K: |(y, x) | t||(, x)||1} exp(-ct2/log2 (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. 2007 American Mathematical Society.