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A Note On the Statistical Difference of Small Direct Products

by Leonid Reyzin

**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 *1/\epsilon*^{4/3}.
Previously known bounds did not
work for few repetitions *l*, requiring *l*>1/*epsilon*^{2}.

This work appears as Boston University Computer Science Technical Report
BUCS-TR-2004-032.