This article gives a survey of recent research related to the Monge-Kantorovich problem.
Principle results are presented on the existence of solutions and their properties both in the …

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 …

In this article, we propose a general framework for distribution-free nonparametric testing in
multi-dimensions, based on a notion of multivariate ranks defined using the theory of …

AMS :: Bulletin of the American Mathematical Society Skip to Main Content American
Mathematical Society American Mathematical Society MathSciNet Bookstore Publications …

В статье дается обзор недавних исследований, связанных с задачей Монжа-
Канторовича. Приведены основные результаты о существовании решений и их …

In this paper we review many aspects of the well-posedness theory for the Cauchy problem
for the continuity and transport equations and for the ordinary differential equation (ODE). In …

In this paper, we study multivariate ranks and quantiles, defined using the theory of optimal
transport, and build on the work of Chernozhukov et al.(Ann. Statist. 45 (2017) 223–256) and …

We establish an improved form of the classical logarithmic Sobolev inequality for the
Gaussian measure restricted to probability densities which satisfy a Poincar\'e inequality …

We describe a construction of Stein kernels using moment maps, which are solutions to a
variant of the Monge–Ampère equation. As a consequence, we show how regularity bounds …