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Optimal transportation distances are valuable for comparing and analyzing probability distributions, but larger-scale computational techniques for the theoretically favorable quadratic case are limited to smooth domains or regularized…
We prove existence and uniqueness results for solutions to a class of optimal transportation problems with infinitely many marginals, supported on the real line. We also provide a characterization of the solution with an explicit formula.…
In this paper, we investigate optimal (partial) transport problems for which the target is a non-convex polygonal domain in \(\mathbb{R}^2\). For the complete optimal transport problem, we prove that the singular set is locally a smooth…
We address the Monge problem in metric spaces with a geodesic distance: (X, d) is a Polish space and dN is a geodesic Borel distance which makes (X,dN) a possibly branching geodesic space. We show that under some assumptions on the…
We establish the validity of asymptotic limits for the general transportation problem between random i.i.d. points and their common distribution, with respect to the squared Euclidean distance cost, in any dimension larger than three.…
We study a general class of elliptic free boundary problems equipped with a Dirichlet boundary condition. Our primary result establishes an optimal $C^{1,1}$-regularity estimate for $L^p$-strong solutions at points where the free and fixed…
We study an optimal transport problem where, at some intermediate time, the mass is accelerated by either an external force field, or self-interacting. We obtain regularity of the velocity potential, intermediate density, and optimal…
In this paper, we prove the existence of classical solutions to second boundary value prob- lems for generated prescribed Jacobian equations, as recently developed by the second author, thereby obtaining extensions of classical solvability…
We discuss equations associated to Cournot-Nash Equilibria as put forward recently by Blanchet and Carlier. These equations are related to an optimal transport problem in which the source measure is known, but the target measure is part of…
The optimal transport problem is studied in the context of Lorentz-Finsler geometry. For globally hyperbolic Lorentz-Finsler spacetimes the first Kantorovich problem and the Monge problem are solved. Further the intermediate regularity of…
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…
Models involving branched structures are employed to describe several supply-demand systems such as the structure of the nerves of a leaf, the system of roots of a tree and the nervous or cardiovascular systems. Given a flow (traffic path)…
We study estimators of the optimal transport (OT) map between two probability distributions. We focus on plugin estimators derived from the OT map between estimates of the underlying distributions. We develop novel stability bounds for OT…
We study a form of optimal transportation surplus functions which arise in hedonic pricing models. We derive a formula for the Ma-Trudinger-Wang curvature of these functions, yielding necessary and sufficient conditions for them to satisfy…
We study the convergence of the transport plans $\gamma_\epsilon$ towards $\gamma_0$ as well as the cost of the entropy-regularized optimal transport $(c,\gamma_\epsilon)$ towards $(c,\gamma_0)$ as the regularization parameter $\epsilon$…
Optimal transport (OT) theory has been been used in machine learning to study and characterize maps that can push-forward efficiently a probability measure onto another. Recent works have drawn inspiration from Brenier's theorem, which…
Energy-minimizing constraint maps are a natural extension of the obstacle problem within a vectorial framework. Due to inherent topological constraints, these maps manifest a diverse structure that includes singularities similar to harmonic…
The Gromov--Wasserstein problem is a non-convex optimization problem over the polytope of transportation plans between two probability measures supported on two spaces, each equipped with a cost function evaluating similarities between…
We give a characterization of optimal transport plans for a variant of the usual quadratic transport cost introduced in [33]. Optimal plans are composition of a deterministic transport given by the gradient of a continuously differentiable…
Let $\Omega$ be a bounded, pseudoconvex domain of $\mathbb C^n$ satisfying the "$f$-Property". The $f$-Property is a consequence of the geometric "type" of the boundary; it holds for all pseudoconvex domains of finite type but may also…