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

E. Hillion, O. T. Johnson

Research output: Contribution to journalArticle (Academic Journal)peer-review

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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 weighted log-concavity. These results are applied to prove the monotone case of the Shepp–Olkin entropy concavity conjecture.
Original languageEnglish
Pages (from-to)276-306
Number of pages31
JournalAnnals of Probability
Issue number1
Publication statusPublished - 2 Feb 2016

Bibliographical note

See arxiv:1303.3381


  • entropy
  • transportation of measures
  • Bernoulli sums
  • concavity

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