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arXiv · 1205.6174

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

David Alonso-Gutierrez·Joscha Prochno
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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.

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David Alonso-Gutierrez, Joscha Prochno. 2012-05-28. On the Gaussian behavior of marginals and the mean width of random polytopes. https://arxiv.org/abs/1205.6174

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