论文标题
非本地瓦斯汀距离：公制和渐近特性
Nonlocal Wasserstein Distance: Metric and Asymptotic Properties
论文作者
论文摘要
Benamou和Brenier的开创性结果提供了Wasserstein距离的表征，这是概率度量空间中最小作用的路径，其中路径是连续性方程的溶液，而动作是动能。在这里，我们考虑了该框架的基本修改，其中路径是非本地（跳跃）连续性方程的解决方案，而动作是非局部动能。由此产生的非局部瓦斯泰尔距离与图形上的分数扩散和瓦斯恒星距离有关。我们表征了距离的基本特性，并在（跳跃）内核上获得了尖锐的条件，该核心指定了非本地运输，这些传输确定拓扑化度是较弱还是强拓扑。本文的关键结果是非局部和局部瓦斯汀距离之间的定量比较。
The seminal result of Benamou and Brenier provides a characterization of the Wasserstein distance as the path of the minimal action in the space of probability measures, where paths are solutions of the continuity equation and the action is the kinetic energy. Here we consider a fundamental modification of the framework where the paths are solutions of nonlocal (jump) continuity equations and the action is a nonlocal kinetic energy. The resulting nonlocal Wasserstein distances are relevant to fractional diffusions and Wasserstein distances on graphs. We characterize the basic properties of the distance and obtain sharp conditions on the (jump) kernel specifying the nonlocal transport that determine whether the topology metrized is the weak or the strong topology. A key result of the paper are the quantitative comparisons between the nonlocal and local Wasserstein distance.
