Geodesics of minimal length in the set of probability measures on graphs
Geodesics of minimal length in the set of probability measures on graphs
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DOI：
10.1051/cocv/2018052
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发表时间：
2019-12-05
影响因子：
1.4
通讯作者：
Mou, Chenchen
中科院分区：
文献类型：
--
作者：
Gangbo, Wilfrid;Li, Wuchen;Mou, Chenchen
我们赋予一个加权图的概率测度集与蒙格-康托洛维奇度量诱导的功能上定义的边缘。假设图有n个顶点，因此概率单形的边界是仿射（n - 2）-链。描述可能与边界相交的最小长度的测地线是我们克服的一个挑战，即使测地线的端点不共享相同的连通分量。这是我们的希望，这项工作将是一个序言的平均场游戏理论的图。
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.