Open Access
2014 $W_{1,+}$-interpolation of probability measures on graphs
Erwan Hillion
Author Affiliations +
Electron. J. Probab. 19: 1-29 (2014). DOI: 10.1214/EJP.v19-3336


We generalize an equation introduced by Benamou and Brenier and characterizing Wasserstein Wp-geodesics for p > 1, from the continuous setting of probability distributions on a Riemannian manifold to the discrete setting of probability distributions on a general graph. Given an initial and a nal distributions (f_0(x)), (f_1(x)), we prove the existence of a curve (f_t(x)) satisfying this Benamou-Brenier equation. We also show that such a curve can be described as a mixture of binomial distributions with respect to a coupling that is solution of a certain optimization problem.


Download Citation

Erwan Hillion. "$W_{1,+}$-interpolation of probability measures on graphs." Electron. J. Probab. 19 1 - 29, 2014.


Accepted: 3 October 2014; Published: 2014
First available in Project Euclid: 4 June 2016

zbMATH: 1347.49077
MathSciNet: MR3272325
Digital Object Identifier: 10.1214/EJP.v19-3336

Primary: 60Dxx
Secondary: 60J10

Keywords: Geometry of Graphs , Optimal transport

Vol.19 • 2014
Back to Top