Related papers: Generalized Talagrand Inequality for Sinkhorn Dist…
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 develop a quantitative contraction framework for Schrodinger and Sinkhorn bridges based on transportation-cost inequalities and Riccati matrix difference equations. Our approach combines logarithmic Sobolev and Talagrand-type…
We give a transport proof of a discrete version of the displacement convexity of entropy on integers (Z), and get, as a consequence, two discrete forms of the Pr{\'e}kopa-Leindler Inequality : the Four Functions Theorem of Ahlswede and…
In this essay, we discuss the notion of optimal transport on geodesic measure spaces and the associated (2-)Wasserstein distance. We then examine displacement convexity of the entropy functional on the space of probability measures. In…
The entropy power inequality (EPI) and the Brascamp-Lieb inequality (BLI) are fundamental inequalities concerning the differential entropies of linear transformations of random vectors. The EPI provides lower bounds for the differential…
The entropy power inequality for independent random vectors is a foundational result of information theory, with deep connections to probability and geometric functional analysis. Several extensions of the entropy power inequality have been…
We study the statistical properties of the entropic optimal (self) transport problem for smooth probability measures. We provide an accurate description of the limit distribution for entropic (self-)potentials and plans as the…
We prove stability estimates for the Shannon-Stam inequality (also known as the entropy-power inequality) for log-concave random vectors in terms of entropy and transportation distance. In particular, we give the first stability estimate…
The goal of the paper is to give an optimal transport formulation of the full Einstein equations of general relativity, linking the (Ricci) curvature of a space-time with the cosmological constant and the energy-momentum tensor. Such an…
We prove a new extremal inequality, motivated by the vector Gaussian broadcast channel and the distributed source coding with a single quadratic distortion constraint problems. As a corollary, this inequality yields a generalization of the…
This paper presents different approaches, based on functional inequalities, to study the speed of convergence in total variation distance of ergodic diffusion processes with initial law satisfying a given integrability condition. To this…
This paper is devoted to results on the Moser-Trudinger-Onofri inequality, or Onofri inequality for brevity. In dimension two this inequality plays a role similar to the Sobolev inequality in higher dimensions. After justifying this…
Optimal transportation distances are a fundamental family of parameterized distances for histograms. Despite their appealing theoretical properties, excellent performance in retrieval tasks and intuitive formulation, their computation…
The paper establishes the equality condition in the I-MMSE proof of the entropy power inequality (EPI). This is done by establishing an exact expression for the deficit between the two sides of the EPI. Interestingly, a necessary condition…
The distance and divergence of the probability measures play a central role in statistics, machine learning, and many other related fields. The Wasserstein distance has received much attention in recent years because of its distinctions…
Understanding the character of electronic excitations is important in computational and reaction mechanistic studies, but their classification from simulations remains an open problem. Distances based on optimal transport have proven very…
We consider the optimal transport problem over convex costs arising from optimal control of linear time-invariant(LTI) systems when the initial and target measures are assumed to be supported on the set of equilibrium points of the LTI…
We develop a full theory for the new class of Optimal Entropy-Transport problems between nonnegative and finite Radon measures in general topological spaces. They arise quite naturally by relaxing the marginal constraints typical of Optimal…
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:…
This paper exploit the equivalence between the Schr\"odinger Bridge problem and the entropy penalized optimal transport in order to find a different approach to the duality, in the spirit of optimal transport. This approach results in a…