Related papers: Transport inequalities for log-concave measures, q…
This note contributes to the understanding of generalized entropy power inequalities. Our main goal is to construct a counter-example regarding monotonicity and entropy comparison of weighted sums of independent identically distributed…
One way to define the concentration of measure phenomenon is via Talagrand inequalities, also called transportation-information inequalities. That is, a comparison of the Wasserstein distance from the given measure to any other absolutely…
We provide a sharp rate of convergence in the central limit theorem for random vectors with an unconditional, log-concave density. The argument relies on analysis of the Neumann laplacian on convex domains and on the theory of optimal…
A general approach for investigating transport phenomena in porous media is presented. This approach has the capacity to represent various kinds of irregularity in porous media without the need for excessive detail or computational effort.…
We consider two methods to establish log-Sobolev inequalities for the invariant measure of a diffusion process when its density is not explicit and the curvature is not positive everywhere. In the first approach, based on the Holley-Stroock…
We prove the transportation inequality with the uniform norm for the laws of diffusion processes with Lipschitz and/or dissipative coefficients and apply them to some singular stochastic differential equations of interest.
In this note we explore how standard statistical distances are equivalent for discrete log-concave distributions. Distances include total variation distance, Wasserstein distance, and $f$-divergences.
We give a simple alternative proof of Royen's Gaussian Correlation inequality by using (a slightly generalized version of) Nakamura-Tsuji's symmetric inverse Brascamp-Lieb inequality for even log-concave functions. We explain that this…
The Boltzmann equation for inelastic Maxwell models is used to determine the Navier-Stokes transport coefficients of a granular binary mixture in $d$ dimensions. The Chapman-Enskog method is applied to solve the Boltzmann equation for…
We consider the Brascamp--Lieb inequalities concerning multilinear integrals of products of functions in several dimensions. We give a complete treatment of the issues of finiteness of the constant, and of the existence and uniqueness of…
We study some special classes of piecewise continuous maps on a finite smooth partition of a compact manifold and look for invariant measures for such maps. We show that in the simplest one-dimensional case (so-called interval translation…
A weighted relative isoperimetric inequality in convex cones is obtained via the Monge-Ampere equation. The method improves several inequalities in the literature, e.g. constants in a theorem of Cabre--Ros--Oton--Serra. Applications are…
This paper studies the log-convexity of the extended beta functions. As a consequence, Tur\'an-type inequalities are established.The monotonicity, log-convexity, log-concavity of extended hypergeometric functions are deduced by using the…
We study in this article the existence and uniqueness of solutions to a class of stochastic transport equations with irregular coefficients. Asking only boundedness of the divergence of the coefficients (a classical condition in both the…
Let $G$ be a countable discrete group with an orthogonal representation $\alpha$ on a real Hilbert space $H$. We prove $L_p$ Poincar\'e inequalities for the group measure space $L_\infty(\Omega_H,\gamma)\rtimes G$, where both the group…
In recent works - both experimental and theoretical - it has been shown how to use computational geometry to efficently construct approximations to the optimal transport map between two given probability measures on Euclidean space, by…
We analyze the transport properties of a neutral tracer in a carrier fluid flowing through percolation-like porous media with spatial correlations. We model convection in the mass transport process using the velocity field obtained by the…
We show that a mixture of Beta distributions has log-concave density whenever the mixing weights are themselves log-concave. Some economic and statistical applications are provided in the last section.
In this paper our aim is to show some mean value inequalities for the modified Bessel functions of the first and second kinds. Our proofs are based on some bounds for the logarithmic derivatives of these functions, which are in fact…
A Langevin equation is proposed to describe the transport of overdamped Brownian particles in a periodic rough potential and driven by an unbiased periodic force. The equation can be transformed into the Fokker-Planck equation by using the…