This is an announcement for the paper "Rate of convergence of random polarizations" by Almut Burchard. 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. Archive classification: math.PR math.FA Remarks: 5 pages Submitted from: almut@math.toronto.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1108.5500 or http://arXiv.org/abs/1108.5500