相关论文: Long-time reverse transportation inequalities for …
We formulate a new information-theoretic principle--the shifted composition rule--which bounds the divergence (e.g., Kullback-Leibler or R\'enyi) between the laws of two stochastic processes via the introduction of auxiliary shifts. In this…
We establish a log-Sobolev inequality for the stationary distribution of mean-field Langevin dynamics with a constant that is independent of the number of particles $N$. Our proof proceeds by establishing the existence of a Lipschitz…
We extend the dimension free Talagrand inequalities for convex distance \cite{talagrand:1995} using an extension of Marton's weak transport \cite{marton:1996a} to other metrics than the Hamming distance. We study the dual form of these weak…
We study the long-time behaviour of both the classical second-order Langevin dynamics and the nonlinear second-order Langevin dynamics of McKean-Vlasov type. By a coupling approach, we establish global contraction in an $L^1$ Wasserstein…
We provide a refined explicit estimate of exponential decay rate of underdamped Langevin dynamics in $L^2$ distance, based on a framework developed in [1]. To achieve this, we first prove a Poincar\'{e}-type inequality with Gibbs measure in…
We establish transportation cost inequalities, with respect to the uniform and $L_2$-metric, on the path space of continuous functions, for laws of solutions of stochastic differential equations with reflections. We also consider the case…
We study hypercontractivity for the underdamped Langevin dynamics with a convex confining potential. Unlike in the overdamped case, the noise acts only on the velocity variable, so the usual argument based on the logarithmic Sobolev…
We present results on the ballistic and diffusive behavior of the Langevin dynamics in a periodic potential that is driven away from equilibrium by a space-time periodic driving force, extending some of the results obtained by Collet and…
We propose a solution for linear inverse problems based on higher-order Langevin diffusion. More precisely, we propose pre-conditioned second-order and third-order Langevin dynamics that provably sample from the posterior distribution of…
Transport of the Brownian particles driven by L\'evy flights coexisting with subdiffusion in asymmetric periodic potentials is investigated in the absence of any external driving forces. Using the Langevin-type dynamics with subordination…
We study the long-time behavior of the underdamped Langevin dynamics, in the case of so-called \emph{weak confinement}. Indeed, any $\mathrm{L}^\infty$ distribution (in position and velocity) relaxes to equilibrium over time, and we…
In this paper we establish the Harnack inequality for globally positive local solutions to a general class of nonlocal in time subdiffusion equations in one space dimension, which includes time-fractional diffusion equations with time order…
Longitudinal nonreciprocal charge transport is usually associated with broken time-reversal symmetry, either from magnetic order or an external magnetic field. Here, we show that it can also arise in nonmagnetic conductors preserving…
We develop the optimal transportation approach to modified log-Sobolev inequalities and to isoperimetric inequalities. Various sufficient conditions for such inequalities are given. Some of them are new even in the classical log-Sobolev…
We develop an instanton approach to the non-equilibrium dynamics in one-dimensional random environments. The long time behavior is controlled by rare fluctuations of the disorder potential and, accordingly, by the tail of the distribution…
This paper studies time-inhomogeneous nonequilibrium diffusion processes, including both Brownian dynamics and Langevin dynamics. We derive upper bounds of the relative entropy production of the time-inhomogeneous process with respect to…
Continuous time random walks and Langevin equations are two classes of stochastic models for describing the dynamics of particles in the natural world. While some of the processes can be conveniently characterized by both of them, more…
This paper studies the continuous-time dynamics generated by control-theoretic Lagrangian methods for equality-constrained optimization. In particular, we consider dynamics induced by proportional-integral and feedback linearization…
We consider stochastic systems involving general -- non-Gaussian and asymmetric -- stable processes. The random quantities, either a stochastic force or a waiting time in a random walk process, explicitly depend on the position. A…
We study the concentration phenomenon for discrete-time random dynamical systems with an unbounded state space. We develop a heuristic approach towards obtaining exponential concentration inequalities for dynamical systems using an entirely…