Related papers: Coupling and Applications
We consider the theoretical properties of a model which encompasses bi-partite matching under transferable utility on the one hand, and hedonic pricing on the other. This framework is intimately connected to tripartite matching problems…
We calculate exact convergence times to reach random bipartite entanglement for various random protocols. The eigenproblem of a Markovian chain governing the process is mapped to a spin chain, thereby obtaining exact expression for the gap…
In many scientific fields imaging is used to relate a certain physical quantity to other dependent variables. Therefore, images can be considered as a map from a real-world coordinate system to the non-negative measurements being acquired.…
Hypergraphs capture multi-way relationships in data, and they have consequently seen a number of applications in higher-order network analysis, computer vision, geometry processing, and machine learning. In this paper, we develop…
We introduce a multivariate version of causal transport, which we name multicausal transport, involving several filtered processes among which causality constraints are imposed. Subsequently, we consider the barycenter problem for…
This paper presents a widely applicable approach to solving (multi-marginal, martingale) optimal transport and related problems via neural networks. The core idea is to penalize the optimization problem in its dual formulation and reduce it…
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…
Transport equations for autonomous driven Fermionic quantum systems are derived with the help of statistical assumptions and of the Markov approximation. The statistical assumptions hold if the system consists of subsystems within which…
Decoupling is a recent development in Fourier analysis, which has applications in harmonic analysis, PDE, and number theory. We survey some applications of decoupling and some of the ideas in the proof. This survey is aimed at a general…
Poissonian ensembles of Markov loops on a finite graph define a random graph process in which the addition of a loop can merge more than two connected components. We study Markov loops on the complete graph derived from a simple random walk…
In this letter, we consider a transportation network with a 100\% penetration rate of connected and automated vehicles (CAVs) and present an optimal routing approach that takes into account the efficiency achieved in the network by…
This paper studies the equitable and optimal transport (EOT) problem, which has many applications such as fair division problems and optimal transport with multiple agents etc. In the discrete distributions case, the EOT problem can be…
In this paper we consider a set of travelers, starting from likely different locations towards a common destination within a road network, and propose solutions to find the optimal connecting points for them. A connecting point is a vertex…
Network Models with couplings between link pairs are the simplest models for a class of networks with Higher Order interactions. In this paper we give an analytic, general solution to this family of Random Graph Models extending previous…
We apply coupling techniques in order to prove that the transfer operators associated with random topological Markov chains and non-stationary shift spaces with the big images and preimages-property have a spectral gap.
This note provides several recent progresses in the study of long time behavior of Markov processes. The examples presented below are related to other scientific fields as PDE's, physics or biology. The involved mathematical tools as…
We examine the use of synchronization as a mechanism for extracting parameter and state information from experimental systems. We focus on important aspects of this problem that have received little attention previously, and we explore them…
In this note, we introduce a class of indicators that enable to compute efficiently optimal transport plans associated to arbitrary distributions of $N$ demands and $N$ supplies in $\mathbf{R}$ in the case where the cost function is…
The study of the packing of a length of wire in a two dimensional domain is done using techniques of conformal maps. The resulting scaling properties are derived through the Coulomb gas formalism of Conformal Field Theories. An analogy is…
Continuum Approximation (CA) is an efficient and parsimonious technique for modeling complex logistics problems. In this paper,we review recent studies that develop CA models for transportation, distribution and logistics problems with the…