Related papers: Transport inequalities for log-concave measures, q…
We define a class of divergences to measure differences between probability density functions in one-dimensional sample space. The construction is based on the convex function with the Jacobi operator of mapping function that pushforwards…
We consider the stochastic transport equation where the randomness is given by the symmetric integral with respect to stochastic measure. For stochastic measure, we assume only $\sigma$-additivity in probability and continuity of paths. The…
Using the method of transportation-information inequality introduced in \cite{GLWY}, we establish Bernstein type's concentration inequalities for empirical means $\frac 1t \int_0^t g(X_s)ds$ where $g$ is a unbounded observable of the…
The linear transport theory is developed to describe the time dependence of the number density of tracer particles in porous media. The advection is taken into account. The transport equation is numerically solved by the analytical discrete…
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.
Anantharam, Jog and Nair recently put forth an entropic inequality which simultaneously generalizes the Shannon-Stam entropy power inequality and the Brascamp-Lieb inequality in entropic form. We give a brief proof of their result based on…
We consider regularized Brascamp-Lieb inequalities using the theory of optimal transportation, more precisely an anisotropic version of Caffarelli's contraction theorem. Furthermore, we provide a full picture concerning the issues of…
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.…
Log-concave distributions include some important distributions such as normal distribution, exponential distribution and so on. In this note, we show inequalities between two Lp-norms for log-concave distributions on the Euclidean space.…
The paper provides an estimate of the total variation distance between distributions of polynomials defined on a space equipped with a logarithmically concave measure in terms of the $L^2$-distance between these polynomials.
Let $\mu$ and $\nu$ be two probability measures on $\R^d$, where $\mu(\d x)= \e^{-V(x)}\d x$ for some $V\in C^1(\R^d)$. Explicit sufficient conditions on $V$ and $\nu$ are presented such that $\mu*\nu$ satisfies the log-Sobolev, Poincar\'e…
In this paper, we extend the scope of Caffarelli's contraction theorem, which provides a measure of the Lipschitz constant for optimal transport maps between log-concave probability densities in $\R^d$. Our focus is on a broader category of…
We establish an improved form of the classical logarithmic Sobolev inequality for the Gaussian measure restricted to probability densities which satisfy a Poincar\'e inequality. The result implies a lower bound on the deficit in terms of…
One among several advantages of measure transport methods is that they allow for a unified framework for processing and analysis of data distributed according to a wide class of probability measures. Within this context, we present results…
Various properties of isoperimetric, functional, Transport-Entropy and concentration inequalities are studied on a Riemannian manifold equipped with a measure, whose generalized Ricci curvature is bounded from below. First, stability of…
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…
Extending results of Harg{\'e} and Hu for the Gaussian measure, we prove inequalities for the covariance Cov$_\mu(f, g)$ where $\mu$ is a general product probability measure on $\mathbb{R}^d$ and $f,g: \mathbb{R}^d \to \mathbb{R}$ satisfy…
In this paper, we use the semi-group method and an adaptation of the $L^2-$method of H\"ormander to establish some $\Phi-$entropy inequalities and asymmetric covariance estimates for the strictly convex measures in $\mathbb R^n$. These…
We use Brascamp-Lieb's inequality to obtain new decoupling inequalities for general Gaussian vectors, and for stationary cyclic Gaussian processes. In the second case, we use a version by Bump and Diaconis of the strong Szego limit theorem.…
In this work we consider dimensional improvements of the logarithmic Sobolev, Talagrand and Brascamp-Lieb inequalities. For this we use optimal transport methods and the Borell-Brascamp-Lieb inequality. These refinements can be written as a…