Progressively applying Gaussian noise transforms complex data distributions to
approximately Gaussian. Reversing this dynamic defines a generative model. When the …

While in principle exact, Kohn–Sham density functional theory—the workhorse of
computational chemistry—must rely on approximations for the exchange–correlation …

This is a comprehensive review of the strong-interaction limit of density functional theory. It
covers the derivation of the limiting strictly correlated electrons (SCE) functional from exact …

In 1931--1932, Erwin Schrödinger studied a hot gas Gedankenexperiment (an instance of
large deviations of the empirical distribution). Schrödinger's problem represents an early …

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 …

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 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 …