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

Abstract : 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.
Type de document :
Pré-publication, Document de travail
2016
Domaine :
Liste complète des métadonnées

Littérature citée [19 références]

https://hal.archives-ouvertes.fr/hal-01286177
Contributeur : Erwan Hillion <>
Soumis le : jeudi 10 mars 2016 - 14:10:04
Dernière modification le : lundi 4 mars 2019 - 14:04:19
Document(s) archivé(s) le : lundi 13 juin 2016 - 08:41:42

### Fichier

1402.3438v1.pdf
Fichiers produits par l'(les) auteur(s)

### Citation

Erwan Hillion. $W_{1,+}$-interpolation of probability measures on graphs. 2016. 〈hal-01286177〉

### Métriques

Consultations de la notice

## 255

Téléchargements de fichiers