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Optimal transport : old and new

Author: Cédric Villani
Publisher: Berlin : Springer, ©2009.
Series: Grundlehren der mathematischen Wissenschaften, 338.
Edition/Format:   Print book : EnglishView all editions and formats
Database:WorldCat
Summary:

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  Read more...

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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Cédric Villani
ISBN: 9783540710493 3540710493
OCLC Number: 244421231
Description: xxii, 973 pages : illustrations ; 24 cm.
Contents: 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.
Series Title: Grundlehren der mathematischen Wissenschaften, 338.
Responsibility: 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 Read more...

 
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