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 The source file(s), subgaussian.tex: 24859 bytes, is(are) stored in gzipped form as 0604299.gz with size 8kb. The corresponding postcript file has gzipped size 54kb. Submitted from: apgiannop@math.uoa.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0604299 or http://arXiv.org/abs/math.FA/0604299 or by email in unzipped form by transmitting an empty message with subject line uget 0604299 or in gzipped form by using subject line get 0604299 to: math@arXiv.org.