Abstract: Dynamical transportation distances are defined between probability measures on the vertices of a graph by means of a discrete analogue of the Benamou—Brenier formula. Independently introduced by Maas (2011) and Mielke (2011), this theory has attracted considerable interest due to its applications to evolution equations and functional inequalities in discrete settings. A key question is how dynamical transportation distances compare to the classical, well-studied Wasserstein distances when the graph is embedded in an Euclidean space. I will present a recent joint work with L. Portinale, which addresses this problem in the previously unexplored case of asymptotically linear energy density, i.e., for transportation functionals resembling the 1-Wasserstein distance. I will also discuss similarities and differences between the discrete counterparts of W1 and W2, in the discrete-to-continuum limit.
Discrete-to-continuum limits of optimal transport with linear growth on periodic graphs
29.01.2025 15:00 - 15:30
Organiser:
SFB 65
Location:
HS 2, EG, OMP 1
Location:
und Zoom
Verwandte Dateien
- pde_afternoon_2025-01-29.pdf 923 KB