Reyzin, Leonid2011-10-202011-10-202004-09-21https://hdl.handle.net/2144/1558We demonstrate that if two probability distributions D and E of sufficiently small min-entropy have statistical difference ε, then the direct-product distributions D^l and E^l have statistical difference at least roughly ε\s√l, provided that l is sufficiently small, smaller than roughly ε^{4/3}. Previously known bounds did not work for few repetitions l, requiring l>ε^2.en-USTechnical Report