Optimal transport for stationary point processes

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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.