This is an announcement for the paper "A note on subgaussian estimates for linear functionals on convex bodies" by Apostolos Giannopoulos, Alain Pajor, and Grigoris Paouris.

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 $$|{ y\in K:,|\langle y,x\rangle |\gr t|\langle\cdot ,x\rangle|_1}|\ls\exp (-ct^2/\log^2(t+1))$$ for all $t\gr 1$, 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.

Archive classification: Functional Analysis; Metric Geometry

Mathematics Subject Classification: 46B07, 52A20

Remarks: 10 pages

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Submitted from: apgiannop@math.uoa.gr

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