Related papers: Transportation-information inequalities for Markov…
A probabilistic method for solving the Monge-Kantorovich mass transport problem on $R^d$ is introduced. A system of empirical measures of independent particles is built in such a way that it obeys a doubly indexed large deviation principle…
Discrete optimal transportation problems arise in various contexts in engineering, the sciences and the social sciences. Often the underlying cost criterion is unknown, or only partly known, and the observed optimal solutions are corrupted…
We construct a transport map from Poisson point processes onto ultra-log-concave measures over the natural numbers, and show that this map is a contraction. Our approach overcomes the known obstacles to transferring functional inequalities…
Optimal transport maps and plans between two absolutely continuous measures $\mu$ and $\nu$ can be approximated by solving semi-discrete or fully-discrete optimal transport problems. These two problems ensue from approximating $\mu$ or both…
We give a new proof of the sharp symmetrized form of Talagrand's transport-entropy inequality. Compared to stochastic proofs of other Gaussian functional inequalities, the new idea here is a certain coupling induced by time-reversed…
For cost functions $c(x,y)=h(x-y)$ with $h\in C^2$ homogeneous of degree $p\geq 2$, we show $L^\infty$-estimates of $Tx-x$ on balls, where $T$ is an $h$-monotone map. Estimates for the interpolating mappings $T_t=t(T-I)+I$ are deduced from…
Recently, CoSi has been identified to have unconventional electronic topology due to lack of inversion center in its B20 cubic structure. The electronic topology has been reported to be present at three nodal points found in the band…
Transportation cost is an attractive similarity measure between probability distributions due to its many useful theoretical properties. However, solving optimal transport exactly can be prohibitively expensive. Therefore, there has been…
We show that Talagrand's transport inequality is equivalent to a restricted logarithmic Sobolev inequality. This result clarifies the links between these two important functional inequalities. As an application, we give the first proof of…
We introduce the proximal optimal transport divergence, a novel discrepancy measure that interpolates between information divergences and optimal transport distances via an infimal convolution formulation. This divergence provides a…
Optimal transport (OT) theory focuses, among all maps $T:\mathbb{R}^d\rightarrow \mathbb{R}^d$ that can morph a probability measure onto another, on those that are the ``thriftiest'', i.e. such that the averaged cost $c(x, T(x))$ between…
We explore a family of information measures that stems from R\'enyi's $\alpha$-Divergences with $\alpha<0$. In particular, we extend the definition of Sibson's $\alpha$-Mutual Information to negative values of $\alpha$ and show several…
We establish an optimal transportation inequality for the Poisson measure on the configuration space. Furthermore, under the Dobrushin uniqueness condition, we obtain a sharp transportation inequality for the Gibbs measure on…
The main result of this paper is the existence of an optimal transport map $T$ between two given measures $\mu$ and $\nu$, for a cost which considers the maximal oscillation of $T$ at scale $\delta$, given by…
We introduce a single-qubit quantum measurement engine fuelled by backaction energy input. To reduce energetic costs associated with information processing, the measurement outcomes are only used with a prescribed laziness probability in…
First-passage properties are central to the kinetics of target-search processes. Theoretical approaches so far primarily focused on predicting first-passage statistics for a given process or model. In practice, however, one faces the…
This paper develops a tractable analytical channel model for first-hitting-time molecular communication (MC) systems under time-varying drift. While existing studies of nonstationary transport rely primarily on numerical solutions of…
This paper presents an information-theoretic approach to address the phasor measurement unit (PMU) placement problem in electric power systems. Different from the conventional 'topological observability' based approaches, this paper…
In this paper we study general transportation problems in $\mathbb{R}^n$, in which $m$ different goods are moved simultaneously. The initial and final positions of the goods are prescribed by measures $\mu^-$, $\mu^+$ on $\mathbb{R}^n$ with…
The data-processing inequality, that is, $I(U;Y) \le I(U;X)$ for a Markov chain $U \to X \to Y$, has been the method of choice for proving impossibility (converse) results in information theory and many other disciplines. Various…