Concavity of entropy along binomial convolutions
Abstract
Motivated by a generalization of Sturm-Lott-Villani theory to discrete spaces and by a conjecture stated by Shepp and Olkin 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 parameters $n\geq 1$ and $t$.
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Pages: 1-9
Publication Date: January 6, 2012
DOI: 10.1214/ECP.v17-1707
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