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

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

2009-03-15

arxiv.org/abs/0903.2634v2

Mathematics

Probability

Scientific paper

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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