Abstract for the talk on 08.06.2018 (11:00 h)
Arbeitsgemeinschaft ANGEWANDTE ANALYSISPeter Gladbach (Universität Leipzig)
Discrete optimal transport: limits and limitations
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.