In this paper, we recover a class of displacement interpolations of probability measures, in the sense of the Optimal Transport theory, by means of semiclassical measures associated with solutions of Schrodinger equation defined on the flat torus. Moreover, we prove the completing viewpoint by proving that a family of displacement interpolations can always be viewed as a path of time-dependent semiclassical measures.
Schrodinger dynamics and optimal transport of measures
Zanelli L.
2021
Abstract
In this paper, we recover a class of displacement interpolations of probability measures, in the sense of the Optimal Transport theory, by means of semiclassical measures associated with solutions of Schrodinger equation defined on the flat torus. Moreover, we prove the completing viewpoint by proving that a family of displacement interpolations can always be viewed as a path of time-dependent semiclassical measures.
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