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arXiv · 0903.2634

A Polynomial Number of Random Points does not Determine the Volume of a Convex Body

Ronen Eldan
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Abstract

We show that there is no algorithm which, provided a polynomial number of random points uniformly distributed over a convex body in R^n, can approximate the volume of the body up to a constant factor with high probability.

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Ronen Eldan. 2011-06-02. A Polynomial Number of Random Points does not Determine the Volume of a Convex Body. https://doi.org/10.1007/s00454-011-9328-x

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