This is an announcement for the paper "On the Gaussian behavior of marginals and the mean width of random polytopes" by David Alonso-Gutierrez and Joscha Prochno.
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 $\R^n$ 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.
Archive classification: math.FA math.PR
Mathematics Subject Classification: 52A22, 52A23, 05D40, 46B09
Submitted from: prochno@math.uni-kiel.de
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1205.6174
or