We consider the problem of estimating the optimal transport map between two probability
distributions, $ P $ and $ Q $ in $\mathbb {R}^ d $, on the basis of iid samples. All existing …

This text develops mathematical foundations for entropic optimal transport and Sinkhorn's
algorithm in a self-contained yet general way. It is a revised version of lecture notes from a …

We study the potential functions that determine the optimal density for ε ε-entropically
regularized optimal transport, the so-called Schrödinger potentials, and their convergence to …

Entropic optimal transport (EOT) presents an effective and computationally viable alternative
to unregularized optimal transport (OT), offering diverse applications for large-scale data …

We study the sample complexity of entropic optimal transport in high dimensions using
computationally efficient plug-in estimators. We significantly advance the state of the art by …

We investigate the convergence rate of the optimal entropic cost v ε to the optimal transport
cost as the noise parameter ε↓ 0. We show that for a large class of cost functions c on R d× …

We study limit theorems for entropic optimal transport (EOT) maps, dual potentials, and the
Sinkhorn divergence. The key technical tool we use is a first and second-order Hadamard …

We study the stability of entropically regularized optimal transport with respect to the
marginals. Lipschitz continuity of the value and Hölder continuity of the optimal coupling in …

We study the stability of entropically regularized optimal transport with respect to the
marginals. Given marginals converging weakly, we establish a strong convergence for the …

We establish the stability of solutions to the entropically regularized optimal transport
problem with respect to the marginals and the cost function. The result is based on the …