相关论文: Quantitative hydrodynamic limits of the Langevin d…
We study the Langevin dynamics corresponding to the $\nabla \varphi$-interface model with a degenerate convex interaction potential satisfying a polynomial growth assumption. Following the work of the author and Armstrong, we interpret…
Hydrodynamic limit for the Ginzburg-Landau $\nabla\phi$ interface model was established in [Nishikawa, 2003] under the Dirichlet boundary conditions. This paper studies the similar problem, but with non-convex potentials. Because of the…
We study the $\nabla \phi$ model with uniformly convex Hamiltonian $\mathcal{H} (\phi) := \sum V(\nabla \phi)$ and prove a quantitative rate of convergence for the finite-volume surface tension as well as a quantitative rate estimate for…
We consider the $\nabla \phi$ interface model with a uniformly convex interaction potential possessing H\"older continuous second derivatives. Combining ideas of Naddaf and Spencer with methods from quantitative homogenization, we show that…
We study a reversible continuous-time Markov dynamics on lozenge tilings of the plane, introduced by Luby et al. Single updates consist in concatenations of $n$ elementary lozenge rotations at adjacent vertices. The dynamics can also be…
We study a reversible continuous-time Markov dynamics of a discrete $(2+1)$-dimensional interface. This can be alternatively viewed as a dynamics of lozenge tilings of the $L\times L$ torus, or as a conservative dynamics for a…
We consider an energy conserving linear dynamics that we perturb by a Glauber dynamics with random site dependent intensity. We prove hydrodynamic limits for this non-reversible system in random media. The diffusion coefficient turns out to…
Starting from the kinetic equations for the fluctuations and correlations of a dilute gas of inelastic hard spheres or disks, a Boltzmann-Langevin equation for the one-particle distribution function of the homogeneous cooling state is…
Hydrodynamic limit for the Ginzburg-Landau $\nabla\phi$ interface model with a conservation law was established in [Nishikawa 2002] under the periodic boundary conditions. This paper studies the same problem on the bounded domain imposing…
This is a review based on the presentation done at the seminar Laurent Schwartz in December 2021. It is announcing results in the forthcoming [Menegaki-Mouhot-Marahrens'22]. This work presents a new simple quantitative method for proving…
We consider models of gradient type, which are the densities of a collection of real-valued random variables $\phi :=\{\phi_x: x \in \Lambda\}$ given by $Z^{-1}\exp({-\sum\nolimits_{j \sim k}V(\phi_j-\phi_k)})$. We focus our study on the…
We study the exponential convergence to the stationary state for nonequilibrium Langevin dynamics, by a perturbative approach based on hypocoercive techniques developed for equilibrium Langevin dynamics. The Hamiltonian and overdamped…
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 introduce and investigate the stochastic dynamics of the density of local extrema (minima and maxima) of non-equilibrium surface fluctuations. We give a number of exact, analytic results for interface fluctuations described by linear…
We derive a quantitative version of the hydrodynamic limit for an interacting particle system inspired by integrate-and-fire neuron models. More precisely, we show that the $L^2$-speed of convergence of the empirical density of states in a…
Previous years researchers began to simulate open quantum system, taking into account the interaction between system and the environment. One approach to deal with this problem is to use the density matrix within the Liouville-von-Neumann…
A multispecies diffuse interface model is formulated in a fluctuating hydrodynamics framework for the purpose of simulating surfactant interfaces at the nanoscale. The model generalizes previous work to ternary mixtures, employing a…
We use the perturbative renormalization group to study classical stochastic processes with memory. We focus on the generalized Langevin dynamics of the \phi^4 Ginzburg-Landau model with additive noise, the correlations of which are local in…
We consider a gradient interface model on the lattice with interaction potential which is a nonconvex perturbation of a convex potential. Using a technique which decouples the neighboring vertices sites into even and odd vertices, we show…
We consider a quantum Langevin kinetic equation for a system of fermions. We first derive the Langevin force noise correlation functions in Landau's Fermi-liquid kinetic theory from general considerations. We then use the resulting equation…