Skip to main content

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

Alonso-Gutiérrez, David; Prochno, Joscha

Authors

David Alonso-Gutiérrez

Joscha Prochno



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.

Journal Article Type Article
Publication Date Jan 1, 2015
Journal Proceedings of the American Mathematical Society
Print ISSN 0002-9939
Electronic ISSN 1088-6826
Publisher American Mathematical Society
Peer Reviewed Peer Reviewed
Volume 143
Issue 2
Pages 821-832
APA6 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
DOI https://doi.org/10.1090/S0002-9939-2014-12401-4
Keywords Supergaussian direction; Random polytope; Orlicz norm; Mean width
Publisher URL http://www.ams.org/journals/proc/2015-143-02/S0002-9939-2014-12401-4/
Copyright Statement ©2018 The authors

Files





You might also like



Downloadable Citations

;