Abstract of a paper by David Alonso-Gutierrez and Joscha Prochno
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 http://arXiv.org/abs/1205.6174
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