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

Abstract

We show that the expected value of the mean width of a random polytope generated by $N$ random vectors ($n\le N\le e^{\sqrt{n}}$) 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.

Cited by in corpus (1)

• On mean outer radii of random polytopes