Entropy Versus Pairwise Independence

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Friday, 10 November 2017, 17:15 to 18:15

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We would discuss the lower bound on the joint entropy of pairwise independent random variables (X_1, ... , X_n) by Lazlo Babai (2013). We know that 2^n - 1 pairwise independent balanced Bernoulli r.v's can be constructed using n independent Bernoulli r.v's. This lower bound shows that this is the best we can do up to a constant factor.