相关论文: Entropy and curvature: beyond the Peres-Tetali con…

Through the consideration of spherically symmetric gravitating systems consisting of perfect fluids with linear equation of state constrained to be in a finite volume, an account is given of the properties of entropy at conditions in which…

We study the existence and long-time asymptotics of weak solutions to a system of two nonlinear drift-diffusion equations that has a gradient flow structure in the Wasserstein distance. The two equations are coupled through a…

We develop a novel stability theory for Sinkhorn semigroups based on Lyapunov techniques and quantitative contraction coefficients, and establish exponential convergence of Sinkhorn iterations on weighted Banach spaces. This…

We offer a new point of view on the (Modified) Log-Sobolev inequality and lower bounds on the Ricci-curvature in the setting where the dynamics are obtained as the limit of Markov processes. In this setting, the large deviation rate…

We establish quantitative stability results for the entropy power inequality (EPI). Specifically, we show that if uniformly log-concave densities nearly saturate the EPI, then they must be close to Gaussian densities in the quadratic…

Continuous-time Markov chains associated to finite-volume discretization schemes of Fokker-Planck equations are constructed. Sufficient conditions under which quantitative exponential decay in the $\phi$-entropy and Wasserstein distance are…

Perturbation theory for Markov chains addresses the question how small differences in the transitions of Markov chains are reflected in differences between their distributions. We prove powerful and flexible bounds on the distance of the…

By using optimal transport theory, we prove a sharp dimension-free isoperimetric inequality involving the volume entropy, in metric measure spaces with non-negative Ricci curvature in the sense of Lott--Sturm--Villani. We show that this…

We provide explicit nonasymptotic estimates for the rate of convergence of empirical means of Markov chains, together with a Gaussian or exponential control on the deviations of empirical means. These estimates hold under a "positive…

The fact that a Markov diffusion semi-group on $\mathbb R^d$ contracts the $L^p$ Wasserstein distance, which has been extensively used to establish uniform-in-time stability estimates (e.g. with respect to numerical discretization errors),…

In the present paper, we prove that a lower bound on the $1$-weighted Ricci curvature is equivalent to a convexity of entropies on the Wasserstein space. Based on such characterization, we provide some interpolation inequalities such as the…

In this paper we establish new simple local geometric criteria for discrete entropic curvature introduced in [47] that are powerful enough to capture many geometric properties of complex models arising in mathematical physics. These results…

The sub-volume scaling of the entanglement entropy with the system's size, $n$, has been a subject of vigorous study in the last decade [1]. The area law provably holds for gapped one dimensional systems [2] and it was believed to be…

In this work we study the long-time behavior for subcritical measure-valued branching processes with immigration on the space of tempered measures. Under some reasonable assumptions on the spatial motion, the branching and immigration…

This paper studies convergence of empirical measures smoothed by a Gaussian kernel. Specifically, consider approximating $P\ast\mathcal{N}_\sigma$, for $\mathcal{N}_\sigma\triangleq\mathcal{N}(0,\sigma^2 \mathrm{I}_d)$, by…

Mostof the existing literature on supervised machine learning problems focuses on the case when the training data set is drawn from an i.i.d. sample. However, many practical problems are characterized by temporal dependence and strong…

We derive geometrical bounds on the irreversibility in both quantum and classical Markovian open systems that satisfy the detailed balance condition. Using information geometry, we prove that irreversible entropy production is bounded from…

Non-convex sampling is a key challenge in machine learning, central to non-convex optimization in deep learning as well as to approximate probabilistic inference. Despite its significance, theoretically there remain many important…

In this paper we consider the convergence of the conditional entropy to the entropy rate for Markov chains. Convergence of certain statistics of long range dependent processes, such as the sample mean, is slow. It has been shown in Carpio…

We study Poisson's equation in the context of general state space Markov chains. For chains satisfying a contraction assumption w.r.t. a Wasserstein distance, we show that a solution exists for Lipschitz functions and investigate its…