We review and formulate results concerning log-concavity and strong-log-concavity in both
discrete and continuous settings. We show how preservation of log-concavity and strongly …

This open access book presents the key aspects of statistics in Wasserstein spaces, ie
statistics in the space of probability measures when endowed with the geometry of optimal …

Why a new book on optimal transport? Were the two books by Fields Medalist Cédric Villani
not enough? And what about the Bible of Gradient Flows, the book by Luigi Ambrosio …

This textbook originated from the teaching experience of the first author at the Scuola
Normale Superiore, where a course on optimal transport and its applications has been given …

This is the first comprehensive introduction to the theory of mass transportation with its many—
and sometimes unexpected—applications. In a novel approach to the subject, the book both …

At the close of the 1980s, the independent contributions of Yann Brenier, Mike Cullen and
John Mather launched a revolution in the venerable field of optimal transport founded by G …

This book deals with a class of mathematical problems which involve the minimization of the
sum of a volume and a surface energy and have lately been refered to as' free discontinuity …

The book is devoted to the theory of gradient flows in the general framework of metric
spaces, and in the more specific setting of the space of probability measures, which provide …

The main purpose of this chapter is to give a derivation, which is mathematically precise,
physically natural, and conceptually simple, of the quasilinear system of partial differential …

This text is an expanded version of the lectures given by the first author in the 2009 CIME
summer school of Cetraro. It provides a quick and reasonably account of the classical theory …