%0 Unpublished work
%T $W_{1,+}$-interpolation of probability measures on graphs
%+ Institut de Mathématiques de Marseille (I2M)
%A Hillion, Erwan
%8 2016-03-10
%D 2016
%R 10.1214/EJP.v19-3336
%Z Mathematics [math]/Probability [math.PR]Preprints, Working Papers, ...
%X We generalize an equation introduced by Benamou and Brenier in [BB00] 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 final distributions (f0(x))x∈G, (f1(x))x∈G, we prove the existence of a curve (ft(k)) t∈[0,1],k∈Z 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.
%G English
%2 https://hal.science/hal-01286177/document
%2 https://hal.science/hal-01286177/file/1402.3438v1.pdf
%L hal-01286177
%U https://hal.science/hal-01286177
%~ CNRS
%~ UNIV-AMU
%~ EC-MARSEILLE
%~ I2M
%~ I2M-2014-