Related papers: Markov Kernels in Optimal Transport via Extending …
Perfect sampling is a technique that uses coupling arguments to provide a sample from the stationary distribution of a Markov chain in a finite time without ever computing the distribution. This technique is very efficient if all the events…
This note exposes the differential topology and geometry underlying some of the basic phenomena of optimal transportation. It surveys basic questions concerning Monge maps and Kantorovich measures: existence and regularity of the former,…
In this article, we develop a kernel-based framework for constructing dynamic, pathdependent trading strategies under a mean-variance optimisation criterion. Building on the theoretical results of (Muca Cirone and Salvi, 2025), we…
We provide a unifying interpretation of various optimal transport problems as a minimisation of a linear functional over the set of all Choquet representations of a given pair of probability measures ordered with respect to a certain convex…
We present several algorithms designed to learn a pattern of correspondence between two data sets in situations where it is desirable to match elements that exhibit a relationship belonging to a known parametric model. In the motivating…
We review two models of optimal transport, where congestion effects during the transport can be possibly taken into account. The first model is Beckmann's one, where the transport activities are modeled by vector fields with given…
We consider probability measures on $\mathbb{R}^{\infty}$ and study optimal transportation mappings for the case of infinite Kantorovich distance. Our examples include 1) quasi-product measures, 2) measures with certain symmetric…
Let $P$ be a Markov kernel on a measurable space $\X$ and let $V:\X\r[1,+\infty)$. We provide various assumptions, based on drift conditions, under which $P$ is quasi-compact on the weighted-supremum Banach space $(\cB_V,\|\cdot\|_V)$ of…
In this work we consider an optimal transport problem with coefficients in a normed Abelian group $G$, and extract a purely intrinsic condition on $G$ that guarantees that the optimal transport (or the corresponding minimum filling) is not…
In this work, we have analyzed the exact closed-form solutions for transport quantities through a mesoscopic region which may be characterized by a polynomial functional of resonant transmission functions. These are then utilized to develop…
During recent decades, there has been a substantial development in optimal mass transport theory and methods. In this work, we consider multi-marginal problems wherein only partial information of each marginal is available, which is a setup…
Optimal transport has numerous applications, particularly in machine learning tasks involving generative models. In practice, the transportation process often encounters an information bottleneck, typically arising from the conversion of a…
In this note we prove that in a metric measure space $(X, d, m)$ verifying the measure contraction property with parameters $K \in \mathbb{R}$ and $1< N< \infty$, any optimal transference plan between two marginal measures is induced by an…
When two Markov operators commute, it suggests that we can couple two copies of one of the corresponding processes. We explicitly construct a number of couplings of this type for a commuting family of Markov processes on the set of…
Many foraging microorganisms rely upon cellular transport networks to deliver nutrients, fluid and organelles between different parts of the organism. Networked organisms ranging from filamentous fungi to slime molds demonstrate a…
Kantorovich potentials denote the dual solutions of the renowned optimal transportation problem. Uniqueness of these solutions is relevant from both a theoretical and an algorithmic point of view, and has recently emerged as a necessary…
Optimal transport has been used extensively in resource matching to promote the efficiency of resources usages by matching sources to targets. However, it requires a significant amount of computations and storage spaces for large-scale…
We introduce the setting of extended metric-topological measure spaces as a general "Wiener-like" framework for optimal transport problems and nonsmooth metric analysis in infinite dimension. After a brief review of optimal transport tools…
This paper focuses on multi-block optimization problems over transport polytopes, which underlie various applications including strongly correlated quantum physics and machine learning. Conventional block coordinate descent-type methods for…
We propose a diffusion approximation method to the continuous-state Markov Decision Processes (MDPs) that can be utilized to address autonomous navigation and control in unstructured off-road environments. In contrast to most…