Geodesics of minimal length in the set of probability measures on graphs

Wilfrid Gangbo; Wuchen Li; Chenchen Mou

doi:10.1051/cocv/2018052

Geodesics of minimal length in the set of probability measures on graphs

Wilfrid Gangbo
, Wuchen Li
, Chenchen Mou^*

^*Corresponding author for this work

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

17 Citations (Scopus)

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 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.

Original language	English
Article number	78
Journal	ESAIM - Control, Optimisation and Calculus of Variations
Volume	25
Online published	5 Dec 2019
DOIs	https://doi.org/10.1051/cocv/2018052
Publication status	Published - Dec 2019
Externally published	Yes

Research Keywords

Geodesic
Hamilton-Jacobi equations on graphs
Manifold with boundary
Optimal transport on simplexes

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title = "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 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.",

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T1 - Geodesics of minimal length in the set of probability measures on graphs

AU - Gangbo, Wilfrid

AU - Li, Wuchen

AU - Mou, Chenchen

PY - 2019/12

Y1 - 2019/12

N2 - 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.

AB - 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.

KW - Geodesic

KW - Hamilton-Jacobi equations on graphs

KW - Manifold with boundary

KW - Optimal transport on simplexes

UR - https://www.scopus.com/pages/publications/85102689819

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85102689819&origin=recordpage

U2 - 10.1051/cocv/2018052

DO - 10.1051/cocv/2018052

M3 - RGC 21 - Publication in refereed journal

SN - 1292-8119

VL - 25

JO - ESAIM - Control, Optimisation and Calculus of Variations

JF - ESAIM - Control, Optimisation and Calculus of Variations

M1 - 78

ER -

Geodesics of minimal length in the set of probability measures on graphs

Abstract

Research Keywords

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