A note on volume thresholds for random polytopes
Metric Geometry
2021-11-16 v2 Probability
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.
Cite
@article{arxiv.2004.01119,
title = {A note on volume thresholds for random polytopes},
author = {Debsoumya Chakraborti and Tomasz Tkocz and Beatrice-Helen Vritsiou},
journal= {arXiv preprint arXiv:2004.01119},
year = {2021}
}