Abstract
We introduce a framework to consider transport problems for integer-valued random variables. We introduce weighting coefficients which allow us to characterize 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 weighted log-concavity. These results are applied to prove the monotone case of the Shepp–Olkin entropy concavity conjecture.
Citation
Erwan Hillion. Oliver Johnson. "Discrete versions of the transport equation and the Shepp–Olkin conjecture." Ann. Probab. 44 (1) 276 - 306, January 2016. https://doi.org/10.1214/14-AOP973
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