Reference : W1,+-interpolation of probability measures on graphs
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/19714
W1,+-interpolation of probability measures on graphs
English
Hillion, Erwan mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
2014
Electronic Journal of Probability
Institute of Mathematical Statistics
19
1-29
Yes (verified by ORBilu)
International
1083-6489
Beachwood
OH
[en] 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.
university of luxembourg
Researchers
http://hdl.handle.net/10993/19714
10.1214/EJP.v19-3336
http://ejp.ejpecp.org/article/view/3336

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