On the distribution of the ψ 2-norm of linear functionals on isotropic convex bodies

@inproceedings{Giannopoulos2011OnTD,
title={On the distribution of the ψ 2-norm of linear functionals on isotropic convex bodies},
author={Andreas Giannopoulos and Grigoris Paouris and P. Valettas},
year={2011}
}

It is known that every isotropic convex bodyK in R has a “subgaussian” direction with constant r = O( √ logn). This follows from the upper bound |Ψ2(K)| 6 c √ logn √ n LK for the volume of the body Ψ2(K) with support function hΨ2(K)(θ) := sup26q6n ‖〈·,θ〉‖q √ q . 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 ψK(t) := σ ( {θ ∈ Sn−1 : hΨ2(K)(θ) 6 ct √ lognLK} ) and we discuss… CONTINUE READING

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