Related papers: The multi-marginal optimal partial transport probl…
We consider a multimarginal transport problem with repulsive cost, where the marginals are all equal to a fixed probability $\rho \in \mathcal{P}(\mathbb{R}^d)$. We prove that, if the concentration of $\rho$ is less than $1/N$, then the…
We consider an optimal transport problem between laws of random probability measures: given a base cost function, we build the associated OT cost between probability measures that in turn we use to define the OT cost between probability…
We analyze several problems of Optimal Transport Theory in the setting of Ergodic Theory. In a certain class of problems we consider questions in Ergodic Transport which are generalizations of the ones in Ergodic Optimization. Another class…
Continuity of the value of the martingale optimal transport problem on the real line w.r.t. its marginals was recently established in Backhoff-Veraguas and Pammer [2] and Wiesel [21]. We present a new perspective of this result using the…
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 study Monge's optimal transportation problem, where the cost is given by optimal control cost. We prove the existence and uniqueness of an optimal map under certain regularity conditions on the Lagrangian, absolute continuity of the…
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…
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…
Semidiscrete optimal transport is a challenging generalization of the classical transportation problem in linear programming. The goal is to design a joint distribution for two random variables (one continuous, one discrete) with fixed…
We study the entropic regularizations of optimal transport problems under suitable summability assumptions on the point-wise transport cost. These summability assumptions already appear in the literature. However, we show that the weakest…
This paper studies the geometry of the optimizer for the optimal transport problem with capacity constraints. We introduce the concept of c-capacity monotonicity, which is a generalization of c-cyclical monotonicity in optimal transport. We…
In this paper we study a variant of the branched transportation problem, that we call multi-material transport problem. This is a transportation problem, where distinct commodities are transported simultaneously along a network. The cost of…
Under mild regularity assumptions, the transport problem is stable in the following sense: if a sequence of optimal transport plans $\pi_1, \pi_2, \ldots$ converges weakly to a transport plan $\pi$, then $\pi$ is also optimal (between its…
This work investigates several aspects related to quantitative stability in optimal transport, as well as uniqueness of the dual transport problem. Our main contributions are as follows. Chapter 1: Observations regarding the quantitative…
We develop a full theory for the new class of Optimal Entropy-Transport problems between nonnegative and finite Radon measures in general topological spaces. They arise quite naturally by relaxing the marginal constraints typical of Optimal…
We study causal optimal transport in continuous time, with Markovian cost, between a finite-state Markov source and a diffusion target. By replacing the source with its conditional law given the observation of the target, we characterize…
We investigate metric conditions that allow to prove existence and uniqueness of a map solving the Monge problem between two marginals in a metric (measure) space, proving two main results. Firstly, we introduce a nonsmooth version of the…
By disintegration of transport plans it is introduced the notion of transport class. This allows to consider the Monge problem as a particular case of the Kantorovich transport problem, once a transport class is fixed. The transport problem…
We consider optimal transportation of measures on metric and topological spaces in the case where the cost function and marginal distributions depend on a parameter with values in a metric space. The Hausdorff distance between the sets of…
Multi-marginal optimal transport plans are concentrated on c-splitting sets. It is known that, similar to the two-marginal case, c-splitting sets are c-cyclically monotone. Within a suitable framework, the converse implication was very…