Rate of convergence of random polarizations

Details Rate of convergence of random polarizations Rate of convergence of random polarizations

2011-08-28

arxiv.org/abs/1108.5500v1

Mathematics

Probability

5 pages

Scientific paper

After n random polarizations of Borel set on a sphere, its expected symmetric
difference from a polar cap is bounded by C/n, where the constant depends on
the dimension [arXiv:1104.4103]. We show here that this power law is best
possible, and that the constant grows at least linearly with the dimension.

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