• xmlui.mirage2.page-structure.header.title
    • français
    • English
  • Help
  • Login
  • Language 
    • Français
    • English
View Item 
  •   BIRD Home
  • CEREMADE (UMR CNRS 7534)
  • CEREMADE : Publications
  • View Item
  •   BIRD Home
  • CEREMADE (UMR CNRS 7534)
  • CEREMADE : Publications
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

Browse

BIRDResearch centres & CollectionsBy Issue DateAuthorsTitlesTypeThis CollectionBy Issue DateAuthorsTitlesType

My Account

LoginRegister

Statistics

Most Popular ItemsStatistics by CountryMost Popular Authors
Thumbnail

Lipschitz Continuity of the Schrödinger Map in Entropic Optimal Transport

Carlier, Guillaume; Chizat, Lenaic; Laborde, Maxime (2022), Lipschitz Continuity of the Schrödinger Map in Entropic Optimal Transport. https://basepub.dauphine.psl.eu/handle/123456789/23105

View/Open
Lipschitz_Schrodinger_Map.pdf (575.4Kb)
Type
Document de travail / Working paper
Date
2022
Series title
Cahier de recherche CEREMADE, Université Paris Dauphine-PSL
Published in
Paris
Pages
18
Metadata
Show full item record
Author(s)
Carlier, Guillaume
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Chizat, Lenaic

Laborde, Maxime
Laboratoire Jacques-Louis Lions [LJLL (UMR_7598)]
Abstract (EN)
The function that maps a family of probability measures to the solution of the dual entropic optimal transport problem is known as the Schrödinger map. We prove that when the cost function is Ck+1 with k in N* then this map is Lipschitz continuous from the L2-Wasserstein space to the space of Ck functions. Our result holds on compact domains and covers the multi-marginal case. As applications, we prove displacement smoothness of the entropic optimal transport cost and the well-posedness of certain Wasserstein gradient flows involving this functional, including the Sinkhorn divergence and a multi-species system.
Subjects / Keywords
Entropic Optimal Transport; Schrödinger map; Wasserstein gradient flows

Related items

Showing items related by title and author.

  • Thumbnail
    On systems of continuity equations with nonlinear diffusion and nonlocal drifts 
    Carlier, Guillaume; Laborde, Maxime (2015-06) Document de travail / Working paper
  • Thumbnail
    A differential approach to the multi-marginal Schrödinger system 
    Carlier, Guillaume; Laborde, Maxime (2020) Article accepté pour publication ou publié
  • Thumbnail
    Convergence of Entropic Schemes for Optimal Transport and Gradient Flows 
    Carlier, Guillaume; Duval, Vincent; Peyré, Gabriel; Schmitzer, Bernhard (2017) Article accepté pour publication ou publié
  • Thumbnail
    Convergence rate of general entropic optimal transport costs 
    Carlier, Guillaume; Pegon, Paul; Tamanini, Luca (2022) Document de travail / Working paper
  • Thumbnail
    Transport optimal de mesures positives : modèles, méthodes numériques, applications 
    Chizat, Lénaïc (2017-11-10) Thèse
Dauphine PSL Bibliothèque logo
Place du Maréchal de Lattre de Tassigny 75775 Paris Cedex 16
Phone: 01 44 05 40 94
Contact
Dauphine PSL logoEQUIS logoCreative Commons logo