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Discrete optimal transport: limits and limitations

  • Peter Gladbach (Universität Leipzig)
A3 01 (Sophus-Lie room)

Abstract

We use the finite volume method to discretely approximate the Kantorovich distance W_2 on the space of probability measures in Euclidean space. This method gives the discrete space a Riemannian structure. However, the question of Gromov-Hausdorff convergence was unanswered except for cubic finite volumes on the torus (Gigli-Maas 2013). We show that the limit distance is in general lower than the Kantorovich distance due to cost-decreasing oscillations. However, under a simple geometric condition on the finite volumes, we show Gromov-Hausdorff convergence.

Katja Heid

MPI for Mathematics in the Sciences Contact via Mail

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