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January 2016 Discrete versions of the transport equation and the Shepp–Olkin conjecture
Erwan Hillion, Oliver Johnson
Ann. Probab. 44(1): 276-306 (January 2016). DOI: 10.1214/14-AOP973


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. "Discrete versions of the transport equation and the Shepp–Olkin conjecture." Ann. Probab. 44 (1) 276 - 306, January 2016.


Received: 1 March 2013; Revised: 1 September 2014; Published: January 2016
First available in Project Euclid: 2 February 2016

zbMATH: 1348.60139
MathSciNet: MR3456338
Digital Object Identifier: 10.1214/14-AOP973

Primary: 60E15 , 60K35
Secondary: 60D99 , 94A17

Keywords: Bernoulli sums , concavity , Entropy , transportation of measures

Rights: Copyright © 2016 Institute of Mathematical Statistics


Vol.44 • No. 1 • January 2016
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