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$W_{1,+}$-interpolation of probability measures on graphs

   
@article{EJP3336,
	author = {Erwan Hillion},
	title = {$W_{1,+}$-interpolation of probability measures on graphs},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {19},
	year = {2014},
	keywords = {Optimal Transport ; Geometry of Graphs},
	abstract = {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.},
	pages = {no. 91, 1-29},
	issn = {1083-6489},
	doi = {10.1214/EJP.v19-3336},    
        url = {http://ejp.ejpecp.org/article/view/3336}}