相关论文: Transportation onto log-Lipschitz perturbations

Two recent works, Avella-Medina and Gonz\'alez-Sanz (2026) and Passeggeri and Paindaveine (2026), studied the robustness of the optimal transport map through its breakdown point, i.e., the smallest fraction of contamination that can make…

We consider an $L^2$-Wasserstein type distance $\rho$ on the configuration space $\Gamma_X$ over a Riemannian manifold $X$, and we prove that $\rho$-Lipschitz functions are contained in a Dirichlet space associated with a measure on…

By using optimal mass transport theory we prove a sharp isoperimetric inequality in ${\sf CD} (0,N)$ metric measure spaces assuming an asymptotic volume growth at infinity. Our result extends recently proven isoperimetric inequalities for…

We employ techniques from optimal transport in order to prove decay of transfer operators associated to iterated functions systems and expanding maps, giving rise to a new proof without requiring a Doeblin-Fortet (or Lasota-Yorke)…

The coordinates along any fixed direction(s), of points on the sphere $S^{n-1}(\sqrt{n})$, roughly follow a standard Gaussian distribution as $n$ approaches infinity. We revisit this classical result from a nonstandard analysis perspective,…

We prove that if a quasiconvex subset $X$ of a metric space $Y$ has finite Nagata dimension and is Lipschitz $k$-connected or admits Euclidean isoperimetric inequalities up to dimension $k$ for some $k$ then $X$ is isoperimetrically…

We study the transport of Gaussian measures under the flow of the 2-dimensional defocusing Schr\"odinger equation $i \partial_t u + \Delta u = |u|^{2k} u$ posed on $\mathbb T^2$. In particular, we show that the Gaussian measures with…

The aim of this work is to investigate semi-Lagrangian approximation schemes on unstructured grids for viscous transport and conservative equations with measurable coefficients that satisfy a one-sided Lipschitz condition. To establish the…

We study the transport properties of the Gaussian measures on Sobolev spaces under the dynamics of the two-dimensional defocusing cubic nonlinear wave equation (NLW). Under some regularity condition, we prove quasi-invariance of the…

We study representations of data from an arbitrary metric space $\mathcal{X}$ in the space of univariate Gaussian mixtures with a transport metric (Delon and Desolneux 2020). We derive embedding guarantees for feature maps implemented by…

Let M and \bar M be n-dimensional manifolds equipped with suitable Borel probability measures \rho and \bar\rho. Ma, Trudinger & Wang gave sufficient conditions on a transportation cost c \in C^4(M \times \bar M) to guarantee smoothness of…

In this article, we generalize the Wasserstein distance to measures with different masses. We study the properties of such distance. In particular, we show that it metrizes weak convergence for tight sequences. We use this generalized…

We study stability under tensorization and projection-type operations of gradient-type estimates and other functional inequalities for Markov semigroups on metric spaces. Using transportation-type inequalities obtained by F. Baudoin and N.…

We introduce Wasserstein-like dynamical transport distances between vector-valued densities on the real line. The mobility function from the scalar theory is replaced by a mobility matrix, that is subject to positivity and concavity…

Optimal Transport has received much attention in Machine Learning as it allows to compare probability distributions by exploiting the geometry of the underlying space. However, in its original formulation, solving this problem suffers from…

In this paper we give a new proof of the (strong) displacement convexity of a class of integral functionals defined on a compact Riemannian manifold satisfying a lower Ricci curvature bound. Our approach does not rely on existence and…

This is the second paper of a series on configuration spaces $\Upsilon$ over singular spaces $X$. Here, we focus on geometric aspects of the extended metric measure space $(\Upsilon, \mathsf{d}_{\Upsilon}, \mu)$ equipped with the…

We study the problem of non-asymptotic deviations between a reference measure and its empirical version, in the 1-Wasserstein metric, under the standing assumption that the measure satisfies a transport-entropy inequality. We extend some…

A multivariate distribution can be described by a triangular transport map from the target distribution to a simple reference distribution. We propose Bayesian nonparametric inference on the transport map by modeling its components using…

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 described as the level sets of solutions to the…