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Article overview
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On the Gaussian behavior of marginals and the mean width of random polytopes | David Alonso-Gutierrez
; Joscha Prochno
; | Date: |
28 May 2012 | Abstract: | We show that the expected value of the mean width of a random polytope
generated by $N$ random vectors ($nleq Nleq e^{sqrt n}$) 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. | Source: | arXiv, 1205.6174 | Services: | Forum | Review | PDF | Favorites |
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