The Annals of Probability
- Ann. Probab.
- Volume 44, Number 1 (2016), 276-306.
Discrete versions of the transport equation and the Shepp–Olkin conjecture
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.
Ann. Probab., Volume 44, Number 1 (2016), 276-306.
Received: March 2013
Revised: September 2014
First available in Project Euclid: 2 February 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60E15: Inequalities; stochastic orderings 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 94A17: Measures of information, entropy 60D99: None of the above, but in this section
Hillion, Erwan; Johnson, Oliver. Discrete versions of the transport equation and the Shepp–Olkin conjecture. Ann. Probab. 44 (2016), no. 1, 276--306. doi:10.1214/14-AOP973. https://projecteuclid.org/euclid.aop/1454423041