Related papers: Free transportation cost inequalities for non-comm…
We address the description of solutes flow with trapping processes in porous media. Starting from a small-scale model for tracer particles trajectories, we derive the corresponding governing equations for the concentration of the mobile and…
We construct approximate transport maps for non-critical Beta-matrix models, that is, maps so that the push forward of a non-critical Beta-matrix model with a given potential is a non-critical Beta-matrix model with another potential, up to…
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…
We show that there is a sharp threshold in dimension one for the transport cost between the Lebesgue measure $\lambda$ and an invariant random measure $\mu$ of unit intensity to be finite. We show that for \emph{any} such random measure the…
We propose an entropic approximation approach for optimal transportation problems with a supremal cost. We establish $\Gamma$-convergence for suitably chosen parameters for the entropic penalization and that this procedure selects…
This article generalizes the study of ramified optimal transport with capacity constraint in transport multi-paths by generalizing the $\mathbf{M}_{\alpha}$ cost to $\mathbf{M}_{\alpha,c}$, which incorporates capacity constraints into the…
Certain trace inequalities related to matrix logarithm are shown. These results enable us to give a partial answer of the open problem conjectured by A.S.Holevo. That is, concavity of the auxiliary function which appears in the random…
Nonlinear response occurs naturally when a strong perturbation takes a system far from equilibrium. Despite of its omnipresence in nanoscale systems, it is difficult to predict in a general and efficient way. Here we introduce a way to…
A general theory is provided delivering convergence of maximal cyclically monotone mappings containing the supports of coupling measures of sequences of pairs of possibly random probability measures on Euclidean space. The theory is based…
Given facilities with capacities and clients with penalties and demands, the transportation problem with market choice consists in finding the minimum-cost way to partition the clients into unserved clients, paying the penalties, and into…
We prove that typical (in the model-free finance setting) price paths with jumps may be uniformly approximated with accuracy $c>0$ by paths whose total variation is of order $1/c.$ A more precise result is obtained for semimartingales with…
General multivariate distributions are notoriously expensive to sample from, particularly the high-dimensional posterior distributions in PDE-constrained inverse problems. This paper develops a sampler for arbitrary continuous multivariate…
Models of spatial firm competition assume that customers are distributed in space and transportation costs are associated with their purchases of products from a small number of firms that are also placed at definite locations. It has been…
Characterization problems in free probability are studied here. Using subordination of free additive and free multiplicative convolutions we generalize some known characterizations in free probability to random variables with unbounded…
The analysis of GPS trajectories is a well-studied problem in Urban Computing and has been used to track people. Analyzing people mobility and identifying the transportation mode used by them is essential for cities that want to reduce…
Consider a multiperiod optimal transport problem where distributions $\mu_{0},\dots,\mu_{n}$ are prescribed and a transport corresponds to a scalar martingale $X$ with marginals $X_{t}\sim\mu_{t}$. We introduce particular couplings called…
We extend the dimension free Talagrand inequalities for convex distance \cite{talagrand:1995} using an extension of Marton's weak transport \cite{marton:1996a} to other metrics than the Hamming distance. We study the dual form of these weak…
Optimal mass transport is described by an approximation of transport cost via semi-discrete costs. The notions of optimal partition and optimal strong partition are given as well. We also suggest an algorithm for computation of Optimal…
In this paper, we investigate the mean squared derivative cost functions that arise in various applications such as in motor control, biometrics and optimal transport theory. We provide qualitative properties, explicit analytical formulas…
We exploit the link between the transport equation and derivatives of expectations to construct efficient pathwise gradient estimators for multivariate distributions. We focus on two main threads. First, we use null solutions of the…