Related papers: The Poisson transport map
We consider the problem to transport resources/mass while abiding by constraints on the flow through constrictions along their path between specified terminal distributions. Constrictions, conceptualized as toll stations at specified…
In recent works - both experimental and theoretical - it has been shown how to use computational geometry to efficently construct approximations to the optimal transport map between two given probability measures on Euclidean space, by…
We prove some theorems on the existence, uniqueness, stability and compactness properties of solutions to inhomogeneous transport equations with Sobolev coefficients, where the inhomogeneous term depends upon the solution through an…
Entropically regularized optimal transport between probability measures supported on compact subsets of Euclidean space admits a representation as an information projection under moment inequality constraints. Exploiting this structure, I…
In this note, we propose a probabilistic approach to bound the (dimension-free) Lipschitz constant of the Langevin flow map on $\mathbb{R}^d$ introduced by Kim and Milman (2012). As example of application, we construct Lipschitz maps from a…
We characterise equality cases in matrix H\"older's inequality and develop a divergence formulation of optimal transport of vector measures. As an application, we reprove the representation formula for measures in the polar cone to monotone…
Bi-log-concavity of probability measures is a univariate extension of the notion of log-concavity that has been recently proposed in a statistical literature. Among other things, it has the nice property from a modelisation perspective to…
We investigate the approximation of Monge--Kantorovich problems on general compact metric spaces, showing that optimal values, plans and maps can be effectively approximated via a fully discrete method. First we approximate optimal values…
We prove a log-Sobolev inequality for a certain class of log-concave measures in high dimension. These are the probability measures supported on the unit cube in R^n whose density takes the form exp(-H) where the function H is assumed to be…
The inverse optimal transport problem is to find the underlying cost function from the knowledge of optimal transport plans. While this amounts to solving a linear inverse problem, in this work we will be concerned with the nonlinear…
We study an optimal weak transport cost related to the notion of convex order between probability measures. On the real line, we show that this weak transport cost is reached for a coupling that does not depend on the underlying cost…
We provide deficit estimates for Nelson's hypercontractivity inequality, the logarithmic Sobolev inequality, and Talagrand's transportation cost inequality under the restriction that the inputs are semi-log-subharmonic, semi-log-convex, or…
We will study variations in Sobolev spaces of optimal transport maps with the standard Gaussian measure as the reference measure. Some dimension free inequalities will be obtained. As application, we construct solutions to Monge-Ampere…
We show that the convolution of a compactly supported measure on $\mathbb{R}$ with a Gaussian measure satisfies a logarithmic Sobolev inequality (LSI). We use this result to give a new proof of a classical result in random matrix theory…
In this paper we extend complex uniform convexity estimates for $\mathbb{C}$ to $ \mathbb{R}^n$ and determine best constants. Furthermore we provide the link to log-Sobolev inequalities and hypercontractivity estimates for ultraspherical…
The optimal (Monge-Kantorovich) transportation problem is discussed from several points of view. The Lagrangian formulation extends the action of the {\em Lagrangian} $L(v,x,t)$ from the set of orbits in $\R^n$ to a set of measure-valued…
In a statistical mechanics model with unbounded spins, we prove uniqueness of the Gibbs measure under various assumptions on finite volume functional inequalities. We follow the approach of G. Royer (1999) and obtain uniqueness by showing…
We give a statistical interpretation of entropic optimal transport by showing that performing maximum-likelihood estimation for Gaussian deconvolution corresponds to calculating a projection with respect to the entropic optimal transport…
We present a flexible method for computing Bayesian optimal experimental designs (BOEDs) for inverse problems with intractable posteriors. The approach is applicable to a wide range of BOED problems and can accommodate various optimality…
In this note, we introduce a class of indicators that enable to compute efficiently optimal transport plans associated to arbitrary distributions of $N$ demands and $N$ supplies in $\mathbf{R}$ in the case where the cost function is…