Search
Talk

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.

Upcoming Events of this Seminar

  • Monday, 14.07.25 tba with Alexandra Holzinger
  • Tuesday, 15.07.25 tba with Anna Shalova
  • Tuesday, 12.08.25 tba with Sarah-Jean Meyer
  • Friday, 15.08.25 tba with Thomas Suchanek
  • Friday, 22.08.25 tba with Nikolay Barashkov
  • Friday, 29.08.25 tba with Andreas Koller