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 …

Sharp asymptotic and finite-sample rates of convergence of empirical measures in Wasserstein
distance Page 1 Bernoulli 25(4A), 2019, 2620–2648 https://doi.org/10.3150/18-BEJ1065 Sharp …

This book describes the latest advances in the theory of mean field games, which are
optimal control problems with a continuum of players, each of them interacting with the …

Let μ _N μ N be the empirical measure associated to a N N-sample of a given probability
distribution μ μ on R^ d R d. We are interested in the rate of convergence of μ _N μ N to μ μ …

The lion's share of this chapter is devoted to the construction of equilibria for mean field
games with a common noise. We develop a general two-step strategy for the search of weak …

Optimal transport maps between two probability distributions $\mu $ and $\nu $ on $\R^ d $
have found extensive applications in both machine learning and statistics. In practice, these …

This work is devoted to the study of rates of convergence of the empirical measures $\mu
_n=\frac {1}{n}\sum _ {k= 1}^ n\delta _ {X_k} $, $ n\geq 1$, over a sample ${(X_k)} _ {k\geq 1} …

Estimation of Wasserstein distances in the Spiked Transport Model Page 1 Bernoulli 28(4),
2022, 2663–2688 https://doi.org/10.3150/21-BEJ1433 Estimation of Wasserstein distances …

We consider empirical measures of R d-valued stochastic process in finite discrete-time. We
show that the adapted empirical measure introduced in the recent work (Ann. Appl. Probab …

We provide upper bounds of the expected Wasserstein distance between a probability
measure and its empirical version, generalizing recent results for finite dimensional …