[en] entropy ; transportation of measures ; Bernoulli sums
[en] We introduce a framework to consider transport problems for integer-valued random variables. We introduce weighting coeffcients which allow us to characterise transport problems in a gradient now setting, and form the basis of our introduction of a discrete version of the Benamou--Brenier formula. Further, we use these coeffcients to state a new form of weighted log-concavity. These results are applied to prove the monotone case of the Shepp--Olkin entropy concavity conjecture.
University of Bristol
EPSRC grant, Information Geometry of Graphs, reference EP/I009450/1.