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 ${\mathbb R}^n$ with volume one and center of mass at the origin, there exists $x\neq 0$ such that $$\{y\in K: < y,x> \gr t\<\cdot, x>\_1\}\ls\exp (ct^2/\log^2(t+1))$$ 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 logconcave measures.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 April 2006
 arXiv:
 arXiv:math/0604299
 Bibcode:
 2006math......4299G
 Keywords:

 Mathematics  Functional Analysis;
 Mathematics  Metric Geometry;
 46B07;
 52A20
 EPrint:
 10 pages