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

• Hillion, Erwan ^[1] ; Johnson, Oliver ^[2]
  1. [1] University of Luxembourg

     University of Luxembourg

     Luxemburgo

     
  2. [2] University of Bristol

     University of Bristol

     Reino Unido

     
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 44, Nº. 1, 2016, págs. 276-306
• Idioma: inglés
• DOI: 10.1214/14-AOP973
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• Resumen

  • 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.