Comment by bjourne

Maybe. "Overall, this only shows us how far on average we go from the original distribution, but the process can only ’terminate’ if the estimated variance at a certain generation becomes small enough, i.e. we effectively turn into a delta function." Iiuc, variance is modeled as a random walk that will sooner or later reach on zero. I'm not sure I buy that because the variance "walks" orders of magnitudes slower than the mean and is much more robust for large sample sizes.