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paper

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

arXiv:0903.2634 · doi:10.1007/s00454-011-9328-x

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.