| Issue |
ESAIM: COCV
Volume 25, 2019
|
|
|---|---|---|
| Article Number | 78 | |
| Number of page(s) | 36 | |
| DOI | https://doi.org/10.1051/cocv/2018052 | |
| Published online | 05 December 2019 | |
Geodesics of minimal length in the set of probability measures on graphs
Department of Mathematics, UCLA,
Los Angeles,
CA
90095, USA.
* Corresponding author: muchenchen@math.ucla.edu
Received:
6
June
2018
Accepted:
24
September
2018
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 have n vertices 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.
Mathematics Subject Classification: 49K35 / 49Q20 / 60J27
Key words: Optimal transport on simplexes / manifold with boundary / Geodesic / Hamilton–Jacobi equations on graphs
© EDP Sciences, SMAI 2019
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