Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

On the Gaussian behavior of marginals and the mean width of random polytopes
HTML articles powered by AMS MathViewer

by David Alonso-Gutiérrez and Joscha Prochno PDF
Proc. Amer. Math. Soc. 143 (2015), 821-832 Request permission

Abstract:

We show that the expected value of the mean width of a random polytope generated by $N$ random vectors ($n\leq N\leq e^{\sqrt n}$) uniformly distributed in an isotropic convex body in $\mathbb {R}^n$ is of the order $\sqrt {\log N} L_K$. 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.
References
Similar Articles
Additional Information
  • David Alonso-Gutiérrez
  • Affiliation: Department of Mathematical and Statistical Sciences, University of Alberta, 505 Central Academic Building, Edmonton T6G 2G1, Canada
  • Address at time of publication: Departament de Matemàtiques, Universitat Jaume I, Campus de Riu Sec, E-12071 Castelló de la Plana, Spain
  • MR Author ID: 840424
  • Email: alonsod@uji.es
  • Joscha Prochno
  • Affiliation: Department of Mathematical and Statistical Sciences, University of Alberta, 605 Central Academic Building, Edmonton T6G 2G1, Canada
  • Address at time of publication: Institute of Analysis, Johannes Keples University, Liuz Altunbergerstr. 69, 4040 Liuz, Austria
  • MR Author ID: 997160
  • Email: prochno@ualberta.ca
  • Received by editor(s): May 28, 2012
  • Received by editor(s) in revised form: March 22, 2013
  • Published electronically: November 3, 2014
  • Communicated by: David Levin
  • © Copyright 2014 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 143 (2015), 821-832
  • MSC (2010): Primary 52A22; Secondary 52A23, 05D40, 46B09
  • DOI: https://doi.org/10.1090/S0002-9939-2014-12401-4
  • MathSciNet review: 3283668