Geodesics of minimal length in the set of probability measures on graphs
Abstract
We endow the set of probability measures on a weighted graph with a Monge–Kantorovich metric induced by a function defined on the set of edges. The graph is assumed to havenvertices and so the boundary of the probability simplex is an affine (n− 2)-chain. Characterizing the geodesics of minimal length which may intersect the boundary is a challenge we overcome even when the endpoints of the geodesics do not share the same connected components. It is our hope that this work will be a preamble to the theory of mean field games on graphs.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jan 01, 2019
- Source ID
- 10.1051/cocv/2018052
Entities
People
- Chenchen Mou
- Wilfrid Gangbo
- Wuchen Li
Organizations
- Air Force Office of Scientific Research
- National Science Foundation