Optimal transport (OT) theory can be informally described using the words of the French
mathematician Gaspard Monge (1746–1818): A worker with a shovel in hand has to move a …

Wasserstein distances are metrics on probability distributions inspired by the problem of
optimal mass transportation. Roughly speaking, they measure the minimal effort required to …

This paper details a general numerical framework to approximate solutions to linear
programs related to optimal transport. The general idea is to introduce an entropic …

In this paper, we introduce a notion of barycenter in the Wasserstein space which
generalizes McCann's interpolation to the case of more than two measures. We provide …

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 paper proposes a new definition of the averaging of discrete probability distributions as
a barycenter over the Monge-Kantorovich optimal transport space. To overcome the time …

This book gives an introduction to basic concepts and methods in mathematical risk
analysis, in particular to those parts of risk theory which are of particular relevance in finance …

In this paper we introduce a Wasserstein-type distance on the set of Gaussian mixture
models. This distance is defined by restricting the set of possible coupling measures in the …

This article introduces a generalization of the discrete optimal transport, with applications to
color image manipulations. This new formulation includes a relaxation of the mass …

This paper exploit the equivalence between the Schrödinger Bridge problem (Léonard in J
Funct Anal 262: 1879–1920, 2012; Nelson in Phys Rev 150: 1079, 1966; Schrödinger in …