Title: A Note On the Statistical Difference of Small Direct Products
Author: Leonid Reyzin
Date: 9/21/04
Abstract: We demonstrate that if two probability distributions D and E of
sufficiently small min-entropy have statistical difference \epsilon, then
the direct-product distributions D^l and E^l have statistical difference
at least roughly \epsilon\sqrt{l}, provided that l is sufficiently small,
smaller than roughly \epsilon^{-4/3}. Previously known bounds did not
work for few repetitions l, requiring l>\epsilon^{-2}.