Related papers: Measure transport via pseudo-cones
The existence of solutions to the Gaussian logarithmic Minkowski problem for C-pseudo-cones is established in this paper. In addition, the non-uniqueness of solutions to the problem is demonstrated.
We prove quantitative bounds on the stability of optimal transport maps and Kantorovich potentials from a fixed source measure $\rho$ under variations of the target measure $\mu$, when the cost function is the squared Riemannian distance on…
Multimarginal optimal transport (MOT) has gained increasing attention in recent years, notably due to its relevance in machine learning and statistics, where one seeks to jointly compare and align multiple probability distributions. This…
We obtain a dual representation of the Kantorovich functional defined for functions on the Skorokhod space using quotient sets. Our representation takes the form of a Choquet capacity generated by martingale measures satisfying additional…
We give a new and constructive proof of the existence of global-in-time weak solutions of the 3-dimensional incompressible semi-geostrophic equations (SG) in geostrophic coordinates, for arbitrary initial measures with compact support. This…
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…
In this paper we consider a scalar transport equation with constant coefficients on domains with discrete space and continuous, discrete or general time. We show that on all these underlying domains solutions of the transport equation can…
A semi-Lagrangian Characteristic Mapping method for the solution of the tracer transport equations on the sphere is presented. The method solves for the solution operator of the equations by approximating the inverse of the diffeomorphism…
This paper is concerned with an optimization problem governed by the Kantorovich optimal transportation problem. This gives rise to a bilevel optimization problem, which can be reformulated as a mathematical problem with complementarity…
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 prove existence of equal area partitions of the unit sphere via optimal transport methods, accompanied by diameter bounds written in terms of Monge--Kantorovich distances. This can be used to obtain bounds on the expectation of the…
By using the fact that the space of all probability measures with finite support can be somehow completed in two different fashions, one generating the Arens-Eells space and another generating the Kantorovich-Wasserstein (Wasserstein-1)…
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…
Existence of solution of the logarithmic Minkowski problem is proved for the case where the discrete measures on the unit sphere satisfy the subspace concentration condition with respect to some special proper subspaces. In order to…
The Kantorovich distance is a widely used metric between probability distributions. The Kantorovich-Rubinstein duality states that it can be defined in two equivalent ways: as a supremum, based on non-expansive functions into [0, 1], and as…
Over the past five years, multi-marginal optimal transport, a generalization of the well known optimal transport problem of Monge and Kantorovich, has begun to attract considerable attention, due in part to a wide variety of emerging…
This paper is devoted to the study of the Monge-Kantorovich theory of optimal mass transport and its applications, in the special case of one-dimensional and circular distributions. More precisely, we study the Monge-Kantorovich distances…
In this note, we study the well-posedness of the Cauchy problem for the transport equation in the BMO space and certain Triebel-Lizorkin spaces.
A recent paper by Cordero-Erausquin and Klartag provides a characterization of the measures $\mu$ on $\R^d$ which can be expressed as the moment measures of suitable convex functions $u$, i.e. are of the form $(\nabla u)\_\\#e^{- u}$ for…
The dual representation of the martingale optimal transport problem in the Skorokhod space of multi dimensional cadlag processes is proved. The dual is a minimization problem with constraints involving stochastic integrals and is similar to…