Rate of convergence of random polarizations
Abstract
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.
 Publication:

arXiv eprints
 Pub Date:
 August 2011
 arXiv:
 arXiv:1108.5500
 Bibcode:
 2011arXiv1108.5500B
 Keywords:

 Mathematics  Probability;
 Mathematics  Functional Analysis;
 60D05 (26D15;
 28A75;
 52A22)
 EPrint:
 5 pages