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Optimal transport : old and new

Autore: Cédric Villani
Editore: Berlin : Springer, cop. 2009.
Serie: Grundlehren der mathematischen Wissenschaften, 338.
Edizione/Formato:   book_printbook : EnglishVedi tutte le edizioni e i formati
Banca dati:WorldCat
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The field of optimal transport has made breathtaking forays into various other domains of mathematics. This book presents a broad overview of this area. PhD students or researchers can read the  Per saperne di più…

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Tipo documento: Book
Tutti gli autori / Collaboratori: Cédric Villani
ISBN: 9783540710493 3540710493
Numero OCLC: 494664787
Note: Contient des exercices.
Descrizione: 1 vol. (XXII-973 p.) : fig. ; 24 cm.
Contenuti: Couplings and changes of variables.- Three examples of coupling techniques.- The founding fathers of optimal transport.- Qualitative description of optimal transport.- Basic properties.- Cyclical monotonicity and Kantorovich duality.- The Wasserstein distances.- Displacement interpolation.- The Monge-Mather shortening principle.- Solution of the Monge problem I: global approach.- Solution of the Monge problem II: Local approach.- The Jacobian equation.- Smoothness.- Qualitative picture.- Optimal transport and Riemannian geometry.- Ricci curvature.- Otto calculus.- Displacement convexity I.- Displacement convexity II.- Volume control.- Density control and local regularity.- Infinitesimal displacement convexity.- Isoperimetric-type inequalities.- Concentration inequalities.- Gradient flows I.- Gradient flows II: Qualitative properties.- Gradient flows III: Functional inequalities.- Synthetic treatment of Ricci curvature.- Analytic and synthetic points of view.- Convergence of metric-measure spaces.- Stability of optimal transport.- Weak Ricci curvature bounds I: Definition and Stability.- Weak Ricci curvature bounds II: Geometric and analytic properties.
Titolo della serie: Grundlehren der mathematischen Wissenschaften, 338.
Altri titoli: Contient des exercices.
Responsabilità: Cédric Villani.
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From the reviews: "The book is aimed to old and new problems of optimal transport. ... This meticulous work is based on very large bibliography ... that is converted into a very valuable monograph Per saperne di più…

 
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