Skip to main content

Research Repository

Advanced Search

On the isotropic constant of random polytopes with vertices on an ℓp-Sphere

Hörrmann, Julia; Prochno, Joscha; Thäle, Christoph

Authors

Julia Hörrmann

Joscha Prochno

Christoph Thäle



Abstract

The symmetric convex hull of random points that are independent and distributed according to the cone probability measure on the p-unit sphere of Rn for some 1 ≤ p < ∞ is considered. We prove that these random polytopes have uniformly absolutely bounded isotropic constants with overwhelming probability. This generalizes the result for the Euclidean sphere (p = 2) obtained by Alonso-Gutiérrez. The proof requires several different tools including a probabilistic representation of the cone measure due to Schechtman and Zinn and moment estimates for sums of independent random variables with log-concave tails originating in a paper of Gluskin and Kwapien.

Citation

Hörrmann, J., Prochno, J., & Thäle, C. (2018). On the isotropic constant of random polytopes with vertices on an ℓp-Sphere. The Journal of geometric analysis, 28(1), 405-426. https://doi.org/10.1007/s12220-017-9826-z

Journal Article Type Article
Acceptance Date May 30, 2016
Online Publication Date Mar 7, 2017
Publication Date Jan 1, 2018
Deposit Date Jun 28, 2018
Journal The Journal of Geometric Analysis
Print ISSN 1050-6926
Publisher Springer Verlag
Peer Reviewed Peer Reviewed
Volume 28
Issue 1
Pages 405-426
DOI https://doi.org/10.1007/s12220-017-9826-z
Keywords Asymptotic convex geometry Cone measure Hyperplane conjecture Isotropic constant ℓp -Sphere Random polytope Stochastic geometry
Public URL https://hull-repository.worktribe.com/output/898805
Publisher URL https://link.springer.com/article/10.1007%2Fs12220-017-9826-z
Contract Date Jun 28, 2018