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

Alonso-Gutiérrez, David; Prochno, Joscha


David Alonso-Gutiérrez

Joscha Prochno


© 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.


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.

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
Electronic ISSN 1088-6826
Publisher American Mathematical Society
Peer Reviewed Peer Reviewed
Volume 143
Issue 2
Pages 821-832
Keywords Supergaussian direction; Random polytope; Orlicz norm; Mean width
Public URL
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