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

Auteur(s): Hillion E.

(Document sans référence bibliographique)

Ref HAL: hal-01286177_v1
DOI: 10.1214/EJP.v19-3336
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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.