Lights and shades of mission work, or, Leaves from a worker's note book : being reminiscenses of seven years service at the capital, 1885-1892 / by B.H.W.

http://www.archive.org/details/lightsandshades00bhwuoft

A Note On the Statistical Difference of Small Direct Products

We 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.