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arXiv · 1109.4464

Comparison of f-vectors of Random Polytopes to the Gaussian Distribution

Sang Du·Mark Syvuk
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Abstract

Choose n random, independent points in R^d according to a fixed distribution. The convex hull of these points is a random polytope. In some cases, central limit theorems have been proven for the components of f-vectors of random polytopes constructed in this and similar ways. In this paper, we provide numerical evidence that the components of the f-vectors of random polytopes generated according to five different distributions are approximately jointly Gaussian for large n.

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Sang Du, Mark Syvuk. 2011-09-21. Comparison of f-vectors of Random Polytopes to the Gaussian Distribution. https://arxiv.org/abs/1109.4464

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