相关论文: Large deviations for the boundary driven symmetric…

We prove the hydrodynamic limit for a particle system in which particles may have different velocities. We assume that we have two infinite reservoirs of particles at the boundary: this is the so-called boundary driven process. The dynamics…

We investigate a boundary-driven Ginzburg-Landau dynamics with long-range interactions. In the hydrodynamic limit, the macroscopic evolution is governed by a fractional heat equation with Dirichlet boundary conditions, while the…

We prove that the stationary measure associated to a boundary driven exclusion process in any dimension satisfies a large deviation principle with rate function given by the quasi potential of the Freidlin and Wentzell theory.

We consider the superposition of a symmetric simple exclusion dynamics, speeded-up in time, with a spin-flip dynamics in a one-dimensional interval with periodic boundary conditions. We prove the large deviations principle for the empirical…

We consider the boundary driven harmonic model, i.e. the Markov process associated to the open integrable XXX chain with non-compact spins. Using the factorial moments we characterize the stationary measure as a mixture of product measures.…

Liquid-gas phase coexistence in a boundary-driven diffusive system is studied by analyzing fluctuating hydrodynamics of a density field defined on a one-dimensional lattice with a space interval $\Lambda$. When an interface width $\ell$ is…

We consider a one-dimensional gradient symmetric exclusion process in mild contact with boundary reservoirs. The hydrodynamic limit of the empirical measure is given by a non-linear second-order parabolic equation with non-linear Robin…

We study the probability of arbitrary density profiles in conserving diffusive fields which are driven by the boundaries. We demonstrate the existence of singularities in the large-deviation functional, the direct analog of the free-energy…

The one-dimensional symmetric exclusion process, the simplest interacting particle process, is a lattice-gas made of particles that hop symmetrically on a discrete line respecting hard-core exclusion. The system is prepared on the infinite…

In this paper, we introduce a mathematical apparatus that is relevant for understanding a dynamical system with small random perturbations and coupled with the so-called transmutation process -- where the latter jumps from one mode to…

We introduce a general framework to describe the stationary state of two driven systems exchanging particles or mass through a contact, in a slow exchange limit. The definition of chemical potentials for the systems in contact requires that…

We consider the superposition of a symmetric simple exclusion dynamics, speeded-up in time, with a spin-flip dynamics in a one-dimensional interval with periodic boundary conditions. We prove the hydrostatics and the dynamical large…

We study a simple transport model driven out of equilibrium by reservoirs at the boundaries, corresponding to the hydrodynamic limit of the symmetric simple exclusion process. We show that a nonlocal transformation of densities and currents…

We consider the weakly asymmetric exclusion process on a bounded interval with particle reservoirs at the endpoints. The hydrodynamic limit for the empirical density, obtained in the diffusive scaling, is given by the viscous Burgers…

In these lectures, we shall present some remarkable results that have been obtained for systems far from equilibrium during the last two decades. We shall put a special emphasis on the concept of large deviation functions that provide us…

We consider a general class of nonlinear diffusive models with bulk dissipation and boundary driving, and derive its hydrodynamic description in the large size limit. Both the average macroscopic behavior and the fluctuating properties of…

We consider the weakly asymmetric exclusion process on a bounded interval with particles reservoirs at the endpoints. The hydrodynamic limit for the empirical density, obtained in the diffusive scaling, is given by the viscous Burgers…

For a class of nonequilibrium systems, called driven lattice gases, we study what happens when two systems are kept in contact and allowed to exchange particles with the total number of particles conserved. Both for attractive and repulsive…

We consider a collection of weakly interacting diffusion processes moving in a two-scale locally periodic environment. We study the large deviations principle of the empirical distribution of the particles' positions in the combined limit…

We consider lattice gas diffusive dynamics with creation-annihilation in the bulk and maintained out of equilibrium by two reservoirs at the boundaries. This stochastic particle system can be viewed as a toy model for granular gases where…