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Concavity of entropy along binomial convolutions. (English) Zbl 1246.60031
Summary: Motivated by a generalization of the Sturm-Lott-Villani theory to discrete spaces and by a conjecture stated by L. A. Shepp and I. Olkin [Contributions to probability, Collect. Pap. dedic. E. Lukacs, 201–206 (1981; Zbl 0534.60020)] about the entropy of sums of Bernoulli random variables, we prove the concavity in \(t\) of the entropy of the convolution of a probability measure \(a\), which has the law of a sum of independent Bernoulli variables, by the binomial measure of the parameters \(n\geq 1\) and \(t\).

60E99 Distribution theory
94A17 Measures of information, entropy
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