Monotonicity Properties of Optimal Transportation¶and the FKG and Related Inequalities
Monotonicity Properties of Optimal Transportation¶and the FKG and Related Inequalities
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最优运输的单调性¶ 以及 FKG 和相关不等式
DOI：
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发表时间：
2000
期刊：
影响因子：
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通讯作者：
L. Caffarelli
中科院分区：
文献类型：
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作者：
L. Caffarelli
翻译后摘要：密度f（X），g（Y）之间的最佳运输可以被解释为一个联合概率分布与边际f（X），和g（Y）。在对f和g的适当假设下，证明了最优运输（Y（X））的单调性和非单调性.作为应用，我们得到了Fortuin，Kasteleyn，Ginibre相关不等式以及Brascamp-Lieb动量不等式的推广.
Abstract: Optimal transportation between densities f(X), g(Y) can be interpreted as a joint probability distribution with marginally f(X), and g(Y). We prove monotonicity and concavity properties of optimal transportation (Y(X)) under suitable assumptions on f and g. As an application we obtain the Fortuin, Kasteleyn, Ginibre correlation inequalities as well as some generalizations of the Brascamp–Lieb momentum inequalities.