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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Showing 1-10 of 24 references

Concentration of mass on convex bodies

View 4 Excerpts
Highly Influenced

Logarithmically concave functions and sections of convex sets in R

K. M. Ball
Studia Math. 88 • 1988
View 4 Excerpts
Highly Influenced

On the volume of caps and bounding the mean-width of an isotropic convex body

P. Pivovarov
Math. Proc. Cambridge Philos. Soc. 149 • 2010
View 1 Excerpt

Centroid Bodies and the Logarithmic Laplace Transform - A Unified Approach , arXiv : 1103 . 2985 v 1 [ 13 ] B . Klartag and R . Vershynin , Small ball probability and Dvoretzky Theorem

L. Lovasz Kannan, M. Simonovits
Israel J . Math . • 2007

On the Ψ2-behavior of linear functionals on isotropic convex bodies

G. Paouris
Studia Math. 168 • 2005
View 1 Excerpt