Optimal transport for stationary point processes

到目前为止，最优输运已经在数学的各个领域得到了广泛的应用，特别是它已经成为分析随机过程、粒子动力学和相关演化方程的有力工具，但主要是在有限维环境中。该项目的目标是在静止点过程或更一般的随机（无限）度量的框架中开发与该理论相对应的理论，并使用这些新工具，例如在无限粒子动力学的分析中或针对感兴趣的特定点过程模型的问题进行攻击。

Optimal transport by now has found manifold applications in various areas of mathematics, in particular it has turned into a powerful tool in the analysis of stochastic processes, particle dynamics, and the associated evolution equations, mostly however in a finite-dimensional setting. The goal of this project is to develop a counterpart to this theory in the framework of stationary point processes or more general random (infinite) measures and to employ these novel tools e.g. in the analysis of infinite particle dynamics or to attack questions for particular point process models of interest.