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arXiv · 2004.01119

A note on volume thresholds for random polytopes

Debsoumya Chakraborti·Tomasz Tkocz·Beatrice-Helen Vritsiou
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Abstract

We study the expected volume of random polytopes generated by taking the convex hull of independent identically distributed points from a given distribution. We show that for log-concave distributions supported on convex bodies, we need at least exponentially many (in dimension) samples for the expected volume to be significant and that super-exponentially many samples suffice for concave measures when their parameter of concavity is positive.

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Debsoumya Chakraborti, Tomasz Tkocz, Beatrice-Helen Vritsiou. 2020-04-02. A note on volume thresholds for random polytopes. https://doi.org/10.1007/s10711-020-00589-5

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