On the Gaussian behavior of marginals and the mean width of random polytopes

Alonso-Gutiérrez, David; Prochno, Joscha

Abstract

© 2014 American Mathematical Society. We show that the expected value of the mean width of a random polytope generated by N random vectors (n ≤ N ≤ e√n) uniformly distributed in an isotropic convex body in ℝnis of the order√logNLK. This completes a result of Dafnis, Giannopoulos and Tsolomitis. We also prove some results in connection with the 1-dimensional marginals of the uniform probability measure on an isotropic convex body, extending the interval in which the average of the distribution functions of those marginals behaves in a sub- or supergaussian way.

Citation

Alonso-Gutiérrez, D., & Prochno, J. (2015). On the Gaussian behavior of marginals and the mean width of random polytopes. Proceedings of the American Mathematical Society, 143(2), 821-832. https://doi.org/10.1090/S0002-9939-2014-12401-4

• Journal Article Type: Article
• Acceptance Date: Mar 22, 2013
• Publication Date: Jan 1, 2015
• Deposit Date: Jun 29, 2018
• Publicly Available Date: Jul 19, 2018
• Journal: Proceedings of the American Mathematical Society
• Print ISSN: 0002-9939
• Publisher: American Mathematical Society
• Peer Reviewed: Peer Reviewed
• Volume: 143
• Issue: 2
• Pages: 821-832
• DOI: https://doi.org/10.1090/S0002-9939-2014-12401-4
• Keywords: Supergaussian direction; Random polytope; Orlicz norm; Mean width
• Public URL: https://hull-repository.worktribe.com/output/900731
• Publisher URL: http://www.ams.org/journals/proc/2015-143-02/S0002-9939-2014-12401-4/
• Contract Date: Jun 29, 2018