Related papers: Homogeneous optimal transport maps between oblique…
We extend the classical regularity theory of optimal transport to non-optimal transport maps generated by heat flow for perturbations of Gaussian measures. Considering probability measures of the form $d\mu(x) = \exp\left(-\frac{|x|^2}{2} +…
Caffarelli's contraction theorem bounds the derivative of the optimal transport map between a log-convex measure and a strongly log-concave measure. We show that an analogous phenomenon holds on the level of the trace: The trace of the…
We consider the problem of optimizing the trajectory of an Unmanned Aerial Vehicle (UAV). Assuming a traffic intensity map of users to be served, the UAV must travel from a given initial location to a final position within a given duration…
Coupling probability measures lies at the core of many problems in statistics and machine learning, from domain adaptation to transfer learning and causal inference. Yet, even when restricted to deterministic transports, such couplings are…
We construct a transport map from Poisson point processes onto ultra-log-concave measures over the natural numbers, and show that this map is a contraction. Our approach overcomes the known obstacles to transferring functional inequalities…
A new pairwise cost function is proposed for the optimal transport barycenter problem, adopting the form of the minimal action between two points, with a Lagrangian that takes into account an underlying probability distribution. Under this…
Optimal transport is widely used to learn distributions, enforce distributional constraints, and model uncertainty. In applications, transport losses are often computed from samples through tractable representations, such as one-dimensional…
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…
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 investigate the optimal transport problem between probability measures when the underlying cost function is understood to satisfy a least action principle, also known as a Lagrangian cost. These generalizations are useful when connecting…
We define upper bound and lower bounds for order-preserving homogeneous of degree one maps on a proper closed cone in $\R^n$ in terms of the cone spectral radius. We also define weak upper and lower bounds for these maps. For a proper…
This paper investigates the optimal transport problem within the framework of Linear Quadratic optimal control systems. We establish the well-posedness of the Monge problem and analyze the regularity of the resulting optimal transport map,…
We prove a central limit theorem for the entropic transportation cost between subgaussian probability measures, centered at the population cost. This is the first result which allows for asymptotically valid inference for entropic optimal…
It is shown that exactly 7 distance-transitive cubic graphs among the existing 12 possess a particular ultrahomogeneous property with respect to oriented cycles realizing the girth that allows the construction of a related Cayley digraph…
We study optimal transportation of measures on compact manifolds for costs defined from convex Lagrangians. We prove that optimal transportation can be interpolated by measured Lipschitz laminations, or geometric currents. The methods are…
We use the transport methods developped in [3] to obtain universality results for local statistics of eigenvalues in the bulk and at the edge for $\beta$-matrix models in the multi-cut regime. We construct an approximate transport map…
We present a systematic study of conditional triangular transport maps in function spaces from the perspective of optimal transportation and with a view towards amortized Bayesian inference. More specifically, we develop a theory of…
Inspired by the matching of supply to demand in logistical problems, the optimal transport (or Monge--Kantorovich) problem involves the matching of probability distributions defined over a geometric domain such as a surface or manifold. In…
We introduce a transport-majorization argument that establishes a majorization in the convex order between two densities, based on control of the gradient of a transportation map between them. As applications, we give elementary derivations…
In this work, we propose a novel machine learning approach to compute the optimal transport map between two continuous distributions from their unpaired samples, based on the DeepParticle methods. The proposed method leads to a min-min…