Related papers: Pseudo-cones and measure transport
We introduce the notion of pseudo-cones of metric spaces as a generalization of both of the tangent cones and the asymptotic cones. We prove that the Assouad dimension of a metric space is bounded from below by that of any pseudo-cone of…
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…
In this paper we propose a gauge-theoretic approach to the problems of optimal mass transport for vector and matrix densities. This resolves both the issues of positivity and action transitivity constraints. Bures-type metrics on the…
We construct homogeneous optimal transport maps for the quadratic cost between convex cones with homogeneous, possibly degenerate, densities when the cones satisfy an obliqueness condition. The existence of such maps plays a central role in…
The general theory for quantum simulation of cubic semiconductor n-MOSFETs is presented within the effective mass equation approach. The full three-dimensional transport problem is described in terms of coupled transverse subband modes…
An open set in C^n is pseudoconvex if and only if its intersection with every affine subspace of complex dimension two as seen as an open set in C^2 is pseudoconvex.
The Foucault pendulum is shown to be an example of motion on a pseudo-surface, and the consequences of that are explored. In particular, its first and second fundamental forms are obtained, as well as its Gaussian and mean curvatures and…
Semi-discrete transport can be characterized in terms of real-valued shifts. Often, but not always, the solution to the shift-characterized problem partitions the continuous region. This paper gives examples of when partitioning fails, and…
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…
We present the fundamentals of a measure transport approach to sampling. The idea is to construct a deterministic coupling---i.e., a transport map---between a complex "target" probability measure of interest and a simpler reference measure.…
We rephrase Monge's optimal transportation (OT) problem with quadratic cost--via a Monge-Amp\`ere equation--as an infinite-dimensional optimization problem, which is in fact a convex problem when the target is a log-concave measure with…
We introduce a concept of optimal transport for vector-valued measures and its dual formulation. In this note we concentrate on the semi-discrete case and show some fundamental differences between the scalar and vector cases. A…
In this second paper, we develop the full mathematical structure of the algebra of the pseudo-observables, in order to solve the quantum measurement problem. Quantum state vectors are recovered but as auxiliary pseudo-observables storing…
We present a range of applications of localisation for constrained transports for pairs of probability measures in order with respect to a lattice cone. These examples comprise irreducible convex paving for martingale transports in…
In this paper we investigate the reverse isoperimetric inequality with respect to the Gaussian measure for convex sets in $\mathbb{R}^{2}$. While the isoperimetric problem for the Gaussian measure is well understood, many relevant aspects…
The calculation of transport profiles from experimental measurements belongs in the category of inverse problems which are known to come with issues of ill-conditioning or singularity. A reformulation of the calculation, the matricial…
The classical problem of optimal transportation can be formulated as a linear optimization problem on a convex domain: among all joint measures with fixed marginals find the optimal one, where optimality is measured against a cost function.…
Caffarelli's contraction theorem states that probability measures with uniformly logconcave densities on R d can be realized as the image of a standard Gaussian measure by a globally Lipschitz transport map. We discuss some counterexamples…
Recently geometric hypergraphs that can be defined by intersections of pseudohalfplanes with a finite point set were defined in a purely combinatorial way. This led to extensions of earlier results about points and halfplanes to…
This paper is devoted to the study of couplings of the Lebesgue measure and the Poisson point process. We prove existence and uniqueness of an optimal coupling whenever the asymptotic mean transportation cost is finite. Moreover, we give…