Concavity of entropy along binomial convolutions
Résumé
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.