В работе дан обзор исследований последнего десятилетия и приведены новые
результаты по различным новым модификациям классической задачи Канторовича …

VI Bogachev, “Kantorovich problem of optimal transportation of measures: new directions of
research”, Uspekhi Mat. Nauk, 77:5(467) (2022), 3–52; Russian Math. Surveys, 77:5 (2022) …

The static optimal transport $(\mathrm {OT}) $ problem between Gaussians seeks to recover
an optimal map, or more generally a coupling, to morph a Gaussian into another. It has been …

We devise a theoretical framework and a numerical method to infer trajectories of a
stochastic process from samples of its temporal marginals. This problem arises in the …

In the recent years the Schrödinger problem has gained a lot of attention because of the
connection, in the small-noise regime, with the Monge-Kantorovich optimal transport …

We study the mean field Schrödinger problem (MFSP), that is the problem of finding the most
likely evolution of a cloud of interacting Brownian particles conditionally on the observation …

In this article, we study the mean field limit of weakly interacting diffusions for confining and
interaction potentials that are not necessarily convex. We explore the relationship between …

We investigate the quadratic Schrödinger bridge problem, aka Entropic Optimal Transport
problem, and obtain weak semiconvexity and semiconcavity bounds on Schrödinger …

Motivated by recent developments in the fields of large deviations for interacting particle
systems and mean field control, we establish a comparison principle for the Hamilton …

The HWI inequality is an “interpolation” inequality between the Entropy H, the Fisher
information I and the Wasserstein distance W. We present a pathwise proof of the HWI …