Related papers: Characterization of Talagrand's transport-entropy …
We present a simple proof of the entropy-power inequality using an optimal transportation argument which takes the form of a simple change of variables. The same argument yields a reverse inequality involving a conditional differential…
We show that elliptic Harnack inequality is stable under form-bounded perturbations for strongly local Dirichlet forms on complete locally compact separable metric spaces that satisfy metric doubling property (or equivalently, relative ball…
We consider, in the Aw-Rascle-Zhang traffic flow model, the problem of the asymptotic stability of constant flows. By using a perturbative approach, we show the stability in a larger space of perturbation than previous results. Furthermore,…
We consider the problem of stability for the Pr\'ekopa-Leindler inequality. Exploiting properties of the transport map between radially decreasing functions and a suitable functional version of the trace inequality, we obtain a uniform…
In this note, we study the well-posedness of the Cauchy problem for the transport equation in the BMO space and certain Triebel-Lizorkin spaces.
We develop a mathematical theory of entropic regularisation of unbalanced optimal transport problems. Focusing on static formulation and relying on the formalism developed for the unregularised case, we show that unbalanced optimal…
We study concentration properties for laws of non-linear Gaussian functionals on metric spaces. Our focus lies on measures with non-Gaussian tail behaviour which are beyond the reach of Talagrand's classical Transportation-Cost Inequalities…
Diffusive cosmic-ray transport in nonuniform large-scale magnetic fields in the presence of boundaries is considered. Reflecting and absorbing boundary conditions are derived for a modified telegraph equation with a convective term.…
New insights into transport properties of nanostructures with a linear dispersion along one direction and a quadratic dispersion along another are obtained by analysing their spectral stability properties under small perturbations.…
In this paper, we develop a general theory for the transport equation within the framework of Triebel-Lizorkin spaces. We first derive commutator estimates in these spaces, dispensing with the conventional divergence-free condition, via the…
We establish elliptic and parabolic Harnack inequalities on graphs with unbounded weights. As an application we prove a local limit theorem for a continuous time random walk $X$ in an environment of ergodic random conductances taking values…
It is known that a quadratic transportation-information inequality $\mathrm{W_2I}$ interpolates between the Talagrand's inequality $\mathrm{W_2H}$ and the log-Sobolev inequality (LSI for short). The aim of the present paper is threefold:…
It is well recognized that interpreting transport experiment results can be challenging when the samples being measured are spatially nonuniform. However, quantitative understanding on the differences between measured and actual transport…
We show that the Hellinger-Kantorovich distance can be expressed as the metric infimal convolution of the Hellinger and the Wasserstein distances, as conjectured by Liero, Mielke, and Savar\'e. To prove it, we study with the tools of…
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…
We study some Hardy-type inequalities involving a general norm in $R^n$ and an anisotropic distance function to the boundary. The case of the optimality of the constants is also addressed.
We establish weak limits for the empirical entropy regularized optimal transport cost, the expectation of the empirical plan and the conditional expectation. Our results require only uniform boundedness of the cost function and no…
We first give a characterization of the L^1-transportation cost-information inequality on a metric space and next find some appropriate sufficient condition to transportation cost-information inequalities for dependent sequences.…
For probability measures on countable spaces we derive distributional limits for empirical entropic optimal transport quantities. More precisely, we show that the empirical optimal transport plan weakly converges to a centered Gaussian…
Recent studies have outlined the interest for the evaluation of transport coefficients in space plasmas, where the observed velocity distributions of plasma particles are conditioned not only by the binary collisions, e.g., at low energies,…