# [Banach] Abstract of a paper by Apostolos Giannopoulos, Alain Pajor, and Grigoris Paouris

Dale Alspach alspach at www.math.okstate.edu
Mon Apr 17 09:42:10 CDT 2006

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 at math.uoa.gr

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http://front.math.ucdavis.edu/math.FA/0604299

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http://arXiv.org/abs/math.FA/0604299

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