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 …

Cet ouvrage offre un panorama sur les inégalités de Sobolev logarithmiques dont le champ
d'application n'a cessé de croıtre au cours des dernieres années, de l'analyse et la …

Diffusion models are a powerful method for generating approximate samples from high-
dimensional data distributions. Several recent results have provided polynomial bounds on …

We strengthen the usual Csiszàr-Kullback-Pinsker in-equality by allowing weights in the
total variation norm; admissible weights depend on the decay of the reference probability …

Abstract We study the Unadjusted Langevin Algorithm (ULA) for sampling from a probability
distribution $\nu= e^{-f} $ on $\R^ n $. We prove a convergence guarantee in Kullback …

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 …

Concentration inequalities deal with deviations of functions of independent random
variables from their expectation. In the last decade new tools have been introduced making …

This book is concerned with the study of the probabilities of very rare events. To understand
why rare events are important at all, one only has to think of a lottery to be convinced that …