This article gives a survey of recent research related to the Monge-Kantorovich problem.
Principle results are presented on the existence of solutions and their properties both in the …

В статье дается обзор недавних исследований, связанных с задачей Монжа-
Канторовича. Приведены основные результаты о существовании решений и их …

Gaussian distributions, along with certain discrete distributions, are the most important
statistical distributions in science and technology. They have been known and used for two …

Let $\gamma $ be the standard Gaussian measure on $\mathbb {R}^ n $ and let $\mathcal
{P} _ {\gamma} $ be the space of probability measures that are absolutely continuous with …

We study the optimal transportation mapping $\nabla\Phi:\mathbb {R}^ d\mapsto\mathbb
{R}^ d $ pushing forward a probability measure $\mu= e^{-V}\dx $ onto another probability …

Let γ be a Gaussian measure on a locally convex space and H be the corresponding
Cameron–Martin space. It has been recently shown by L. Ambrosio and A. Figalli that the …

According to a classical result of E. Calabi any hyperbolic affine hypersphere endowed with
its natural Hessian metric has a non-positive Ricci tensor. The affine hyperspheres can be …

We consider probability measures on R∞ and study optimal transportation mappings for the
case of infinite Kantorovich distance. Our examples include (1) quasiproduct measures and …

We prove that, for the distributions of one-dimensional diffusions with nonconstant diffusion
coefficients, the Monge and Kantorovich problems associated with the cost function …

In this work, we will take the standard Gaussian measure as the reference measure and
study the variation of optimal transport maps in Sobolev spaces with respect to it; as a by …