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We introduce a framework to consider transport problems for integer-valued random variables. We introduce weighting coefficients which allow us to characterise transport problems in a gradient flow setting, and form the basis of our introduction of a discrete version of the Benamou–Brenier formula. Further, we use these coefficients to state a new form of… (More)

We prove the Shepp–Olkin conjecture, which states that the entropy of the sum of independent Bernoulli random variables is concave in the parameters of the individual random variables. Our proof is a refinement of an argument previously presented by the same authors, which resolved the conjecture in the monotonic case (where all the parameters are… (More)

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