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On the Wasserstein distance between mutually singular measures

hal.structure.identifierDipartimento di Matematica [Pisa]
dc.contributor.authorButtazzo, Giuseppe*
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorCarlier, Guillaume*
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorLaborde, Maxime*
dc.date.accessioned2017-11-06T10:13:13Z
dc.date.available2017-11-06T10:13:13Z
dc.date.issued2018
dc.identifier.issn1864-8258
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/16916
dc.language.isoenen
dc.subjectWasserstein distance
dc.subjectsingular measures
dc.subjectperimeter penalization
dc.subject.ddc515en
dc.titleOn the Wasserstein distance between mutually singular measures
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe study the Wasserstein distance between two measures µ, ν which are mutually singular. In particular, we are interested in minimization problems of the form W (µ, A) = inf W (µ, ν) : ν ∈ A where µ is a given probability and A is contained in the class µ ⊥ of probabilities that are singular with respect to µ. Several cases for A are considered; in particular, when A consists of L 1 densities bounded by a constant, the optimal solution is given by the characteristic function of a domain. Some regularity properties of these optimal domains are also studied. Some numerical simulations are included, as well as the double minimization problem min P (B) + kW (A, B) : |A ∩ B| = 0, |A| = |B| = 1 , where k > 0 is a fixed constant, P (A) is the perimeter of A, and both sets A, B may vary.
dc.relation.isversionofjnlnameAdvances in Calculus of Variations
dc.relation.isversionofjnlvol13
dc.relation.isversionofjnlissue2
dc.relation.isversionofjnldate2018
dc.relation.isversionofjnlpages141–154
dc.relation.isversionofdoi10.1515/acv-2017-0036
dc.relation.isversionofjnlpublisherDe Gruyter
dc.subject.ddclabelAnalyseen
dc.description.ssrncandidatenon
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dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2020-07-01T12:05:25Z
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