Wasserstein barycenters on metric graphs
J\'er\^ome Bertrand (IMT), Jianyu Ma (IMT)
TL;DR
This paper studies conditions under which Wasserstein barycenters on metric graphs are absolutely continuous relative to the Hausdorff measure, excluding the vertices.
Contribution
It establishes specific conditions ensuring the absolute continuity of Wasserstein barycenters on metric graphs away from vertices.
Findings
Wasserstein barycenters can be absolutely continuous on metric graphs.
Conditions are identified for absolute continuity away from vertices.
The results clarify the structure of barycenters on graphs.
Abstract
In this paper we provide conditions for a Wasserstein barycenter to be absolutely continuous with respect to its Hausdorff measure away from the vertices of the graph.
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