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

Erwan Hillion (1) , Oliver Johnson (2)

1 I2M - Institut de Mathématiques de Marseille
2 University of Bristol [Bristol]

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.

Domaines: Probabilités [math.PR]

Erwan Hillion, Oliver Johnson. Discrete versions of the transport equation and the Shepp-Olkin conjecture. Annals of Probability, 2016, 44 (1), ⟨10.1214/14-AOP973⟩. ⟨hal-01296786⟩