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In this paper, one investigates the following type of transportation-information $T_cI$ inequalities: $\alpha(T_c(\nu,\mu))\le I(\nu|\mu)$ for all probability measures $\nu$ on some metric space $(\XX, d)$, where $\mu$ is a given…

Probability · Mathematics 2010-04-13 Arnaud Guillin , Christian Leonard , Liming Wu , Nian Yao

Let $(X_1,\dots,X_m)$ be self-adjoint non-commutative random variables distributed according to the free Gibbs law given by a sufficiently regular convex and semi-concave potential $V$, and let $(S_1,\dots,S_m)$ be a free semicircular…

Operator Algebras · Mathematics 2020-01-08 David Jekel

Motivated by recent work of Au, C{\'e}bron, Dahlqvist, Gabriel, and Male, we study regularity properties of the distribution of a sum of two selfad-joint random variables in a tracial noncommutative probability space which are free over a…

Operator Algebras · Mathematics 2018-11-12 Serban Belinschi

We study the optimal transport problem in the Euclidean space where the cost function is given by the value function associated with a Linear Quadratic minimization problem. Under appropriate assumptions, we generalize Brenier's Theorem…

Optimization and Control · Mathematics 2011-05-23 Ahed Hindawi , Ludovic Rifford , Jean-Baptiste Pomet

Given two probability measures on sequential data, we investigate the transport problem with time-inconsistent preferences in a discrete-time setting. Motivating examples are nonlinear objectives, state-dependent costs, and regularized…

Optimization and Control · Mathematics 2025-06-23 Erhan Bayraktar , Bingyan Han

Optimal transport (OT) formalizes the problem of finding an optimal coupling between probability measures given a cost matrix. The inverse problem of inferring the cost given a coupling is Inverse Optimal Transport (IOT). IOT is less well…

Machine Learning · Statistics 2022-06-22 Wei-Ting Chiu , Pei Wang , Patrick Shafto

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.…

Computer Vision and Pattern Recognition · Computer Science 2018-04-18 Liam Cattell , Gustavo K. Rohde

In this paper, we give estimates of the quadratic transportation cost in the conditional central limit theorem for a large class of dependent sequences. Applications to irreducible Markov chains, dynamical systems generated by intermittent…

Probability · Mathematics 2022-12-09 Jérôme Dedecker , Florence Merlevède , Emmanuel Rio

For probability measures on a complete separable metric space, we present sufficient conditions for the existence of a solution to the Kantorovich transportation problem. We also obtain sufficient conditions (which sometimes also become…

Probability · Mathematics 2007-06-13 S. Ekisheva , C. Houdré

Optimal transport (OT) based data analysis is often faced with the issue that the underlying cost function is (partially) unknown. This paper is concerned with the derivation of distributional limits for the empirical OT value when the cost…

Statistics Theory · Mathematics 2023-01-05 Shayan Hundrieser , Gilles Mordant , Christoph Alexander Weitkamp , Axel Munk

We propose a nonlinear difference-in-differences method to estimate multivariate counterfactual distributions in classical treatment and control study designs with observational data. Our approach sheds a new light on existing approaches…

Methodology · Statistics 2024-03-11 William Torous , Florian Gunsilius , Philippe Rigollet

Using the growing volumes of vehicle trajectory data, it becomes increasingly possible to capture time-varying and uncertain travel costs in a road network, including travel time and fuel consumption. The current paradigm represents a road…

Databases · Computer Science 2015-12-07 Jian Dai , Bin Yang , Chenjuan Guo , Christian S. Jensen

We review some simple techniques based on monotone mass transport that allow to obtain transport-type inequalities for any log-concave probability measure, and for more general measures as well. We discuss quantitative forms of these…

Probability · Mathematics 2016-06-14 Dario Cordero-Erausquin

In the Monge-Kantorovich transport problem, the transport cost is expressed in terms of transport maps or transport plans, which play crucial roles there. A variant of the Monge-Kantorovich problem is the ramified (branching) transport…

Analysis of PDEs · Mathematics 2023-10-09 Qinglan Xia , Haotian Sun

Previous proposals to permit non-exponential free-path statistics in radiative transfer have not included support for volume and boundary sources that are spatially uncorrelated from the scattering events in the medium. Birth-collision free…

Computational Physics · Physics 2021-02-19 Eugene d'Eon

We consider the problem of transporting \nota{one probability measure into another through} the flow of a given driftless control-affine system. Under suitable regularity conditions, the controllability of the system by means of open-loop…

Optimization and Control · Mathematics 2025-06-23 Marco Caponigro , Arianna Vicari

We study an optimal weak transport cost related to the notion of convex order between probability measures. On the real line, we show that this weak transport cost is reached for a coupling that does not depend on the underlying cost…

Probability · Mathematics 2015-12-25 Nathael Gozlan , Cyril Roberto , Paul-Marie Samson , Yan Shu , Prasad Tetali

We consider the problem of optimal transportation with quadratic cost between a empirical measure and a general target probability on R d , with d $\ge$ 1. We provide new results on the uniqueness and stability of the associated optimal…

Probability · Mathematics 2018-03-12 Eustasio Del Barrio , Jean-Michel Loubes

In this paper, we established a quadratic transportation cost inequality for scalar stochastic conservation laws driven by multiplicative noise. The doubling variables method plays an important role.

Probability · Mathematics 2021-01-01 Rangrang Zhang , Tusheng Zhang

We use the transport methods developped in [3] to obtain universality results for local statistics of eigenvalues in the bulk and at the edge for $\beta$-matrix models in the multi-cut regime. We construct an approximate transport map…

Probability · Mathematics 2017-08-04 Florent Bekerman