相关论文: Weighted $L^2$-contractivity of Langevin dynamics …

In non-equilibrium statistical physics models, the invariant measure $\mu$ of the process does not have an explicit density. In particular the adjoint $L^*$ in $L^2(\mu)$ of the generator $L$ is unknown and many classical techniques fail in…

First weak solutions of generalized stochastic Hamiltonian systems (gsHs) are constructed via essential m-dissipativity of their generators on a suitable core. For a scaled gsHs we prove convergence of the corresponding semigroups and…

In this paper, we study systems of $N$ interacting particles described by the classical and relativistic Langevin dynamics with singular forces and multiplicative noises. For the classical model, we prove the ergodicity, obtaining an…

We consider the convergence of kinetic Langevin dynamics to its ergodic invariant measure, which is Gibbs distribution. Instead of the standard setup where the friction coefficient is a constant scalar, we investigate position-dependent…

We construct an infinite particle/infinite volume Langevin dynamics on the space of configurations in $\R^d$ having velocities as marks. The construction is done via a limiting procedure using $N$-particle dynamics in cubes…

The classical (overdamped) Langevin dynamics provide a natural algorithm for sampling from its invariant measure, which uniquely minimizes an energy functional over the space of probability measures, and which concentrates around the…

We unify the variational hypocoercivity framework established by D. Albritton, S. Armstrong, J.-C. Mourrat, and M. Novack, with the notion of second-order lifts of reversible diffusion processes, recently introduced by A. Eberle and F.…

Discretization of continuous-time diffusion processes is a widely recognized method for sampling. However, it seems to be a considerable restriction when the potentials are often required to be smooth (gradient Lipschitz). This paper…

Langevin dynamics has found a large number of applications in sampling, optimization and estimation. Preconditioning the gradient in the dynamics with the covariance - an idea that originated in literature related to solving estimation and…

We establish the first connection between $2d$ Liouville quantum gravity and natural dynamics of random matrices. In particular, we show that if $(U_t)$ is a Brownian motion on the unitary group at equilibrium, then the measures $$…

The paper concerns $L^1$- convergence to equilibrium for weak solutions of the spatially homogeneous Boltzmann Equation for soft potentials $(-4\le \gm<0$), with and without angular cutoff. We prove the time-averaged $L^1$-convergence to…

By the probabilistic coupling approach which combines a new refined basic coupling with the synchronous coupling for L\'evy processes, we obtain explicit exponential contraction rates in terms of the standard $L^1$-Wasserstein distance for…

This paper deals with the long time behaviour of solutions to the spatially homogeneous Landau equation with hard potentials . We prove an exponential in time convergence towards the equilibrium with the optimal rate given by the spectral…

This paper is concerned with the long time behavior of Langevin dynamics of {\em Coulomb gases} in $\mathbf{R}^d$ with $d\geq 2$, that is a second order system of Brownian particles driven by an external force and a pairwise repulsive…

The convergence of the kinetic Langevin simulated annealing is proven under mild assumptions on the potential $U$ for slow logarithmic cooling schedules. Moreover, non-convergence for fast logarithmic and non-logarithmic cooling schedules…

We study the convergence in total variation and $V$-norm of discretization schemes of the underdamped Langevin dynamics. Such algorithms are very popular and commonly used in molecular dynamics and computational statistics to…

In this paper, we propose a second-order continuous primal-dual dynamical system with time-dependent positive damping terms for a separable convex optimization problem with linear equality constraints. By the Lyapunov function approach, we…

Priors with non-smooth log-densities, such as the l1-prior, are widely used in Bayesian inverse problems for their sparsity-inducing properties. Existing Langevin-based sampling methods typically rely on proximal mappings or smooth…

It is well know that for globally contractive autonomous systems, there exists a unique equilibrium and the distance to the equilibrium evaluated along any trajectory decreases exponentially with time. We show that, additionally, the…

This article is concerned with sampling from Gibbs distributions $\pi(x)\propto e^{-U(x)}$ using Markov chain Monte Carlo methods. In particular, we investigate Langevin dynamics in the continuous- and the discrete-time setting for such…