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


 
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1. Title Title of document $W_{1,+}$-interpolation of probability measures on graphs
 
2. Creator Author's name, affiliation, country Erwan Hillion; University of Luxembourg; Luxembourg
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Optimal Transport ; Geometry of Graphs
 
3. Subject Subject classification 60Dxx ; 60J10
 
4. Description 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.
 
5. Publisher Organizing agency, location
 
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7. Date (YYYY-MM-DD) 2014-10-03
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/3336
 
10. Identifier Digital Object Identifier 10.1214/EJP.v19-3336
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 19
 
12. Language English=en en
 
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