DISCRETE VERSIONS OF THE TRANSPORT EQUATION AND THE SHEPP-OLKIN CONJECTURE

• 成果类型: Article
• 署名作者: Hillion, Erwan; Johnson, Oliver
• 署名单位: University of Luxembourg; Aix-Marseille Universite; University of Bristol
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/14-AOP973
• 发表日期: 2016
• 页码: 276-306
• 关键词: metric-measure-spaces; entropy; geometry; LAW

摘要

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.