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arXiv · 1802.04089

Threshold phenomena for high-dimensional random polytopes

Gilles Bonnet·Giorgos Chasapis·Julian Grote·Daniel Temesvari·Nicola Turchi
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Abstract

Let $X_1,\ldots,X_N$, $N>n$, be independent random points in $\mathbb{R}^n$, distributed according to the so-called beta or beta-prime distribution, respectively. We establish threshold phenomena for the volume, intrinsic volumes, or more general measures of the convex hulls of these random point sets, as the space dimension $n$ tends to infinity. The dual setting of polytopes generated by random halfspaces is also investigated.

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Gilles Bonnet, Giorgos Chasapis, Julian Grote, Daniel Temesvari, Nicola Turchi. 2018-02-12. Threshold phenomena for high-dimensional random polytopes. https://doi.org/10.1142/s0219199718500384

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