论文标题
弱运输理论的应用
Applications of weak transport theory
论文作者
论文摘要
Gozlan，Roberto，Samson和Tetali是由应用于几何不平等的应用，引入了“弱”成本功能的运输问题。最佳运输理论的基本结果可以扩展到显着的一般性。在本文中，我们从不同领域收集了几个问题，这些问题可以在弱运输理论的框架中重铸，即：Schrödinger问题，Brenier-Strassen Theorem，最佳机制设计，线性转移和Semimartingale Transport。我们的观点产生了一种统一的方法，并且通常可以增强原始结果。
Motivated by applications to geometric inequalities, Gozlan, Roberto, Samson, and Tetali introduced a transport problem for `weak' cost functionals. Basic results of optimal transport theory can be extended to this setup in remarkable generality. In this article we collect several problems from different areas that can be recast in the framework of weak transport theory, namely: the Schrödinger problem, the Brenier-Strassen theorem, optimal mechanism design, linear transfers and semimartingale transport. Our viewpoint yields a unified approach and often allows to strengthen the original results.
