Zusammenfassung für den Vortrag am 08.06.2018 (11:00 Uhr)

Arbeitsgemeinschaft ANGEWANDTE ANALYSIS

Peter 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.


10.06.2018, 02:30