An Invitation To Optimal Transport Wasserstein Distances And Gradient Flows
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An Invitation to Optimal Transport, Wasserstein Distances, and Gradient Flows
Author | : Alessio Figalli |
Publisher | : European Mathematical Society |
Total Pages | : 0 |
Release | : 2023-05-15 |
Genre | : Mathematics |
ISBN | : 3985470502 |
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This book provides a self-contained introduction to optimal transport, and it is intended as a starting point for any researcher who wants to enter into this beautiful subject. The presentation focuses on the essential topics of the theory: Kantorovich duality, existence and uniqueness of optimal transport maps, Wasserstein distances, the JKO scheme, Otto's calculus, and Wasserstein gradient flows. At the end, a presentation of some selected applications of optimal transport is given. Suitable for a course at the graduate level, the book also includes an appendix with a series of exercises along with their solutions. The second edition contains a number of additions, such as a new section on the Brunn–Minkowski inequality, new exercises, and various corrections throughout the text.
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