On the distribution of the ψ2-norm of linear functionals on isotropic convex bodies

Abstract

It is known that every isotropic convex body K in Rn has a subgaussian direction with constant This follows from the upper bound for the volume of the body Ψ 2(K) with support function . The approach in all the related works does not provide estimates on the measure of directions satisfying a ψ2-estimate with a given constant r. We introduce the function and we discuss lower bounds for ψ K (t), Information on the distribution of the ψ2-norm of linear functionals is closely related to the problem of bounding from above the mean width of isotropic convex bodies. © 2012 Springer-Verlag Berlin Heidelberg.