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arXiv · 1303.3381

Discrete versions of the transport equation and the Shepp-Olkin conjecture

Erwan Hillion·Oliver Johnson
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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.

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Erwan Hillion, Oliver Johnson. 2016-02-22. Discrete versions of the transport equation and the Shepp-Olkin conjecture. https://doi.org/10.1214/14-aop973

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