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How low can the joint entropy of
-wise independent (for ) discrete random variables be, subject to given constraints on the individual distributions (say, no value may be taken by a variable with probability greater than , for )? This question has been posed and partially answered in a recent work of Babai [Entropy versus pairwise independence (preliminary version), http://people.cs.uchicago.edu/ laci/papers/13augEntropy.pdf, 2013]. In this paper we improve some of his bounds,...
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