Non-equilibrium Fluctuations of Interacting Particle Systems

Abstract

We obtain the large scale limit of the fluctuations around its hydrodynamic limit of the density of particles of a weakly asymmetric exclusion process in dimension up to three. The proof is based upon a sharp estimate on the relative entropy of the law of the process with respect to product reference measures associated to the hydrodynamic limit profile, which holds in any dimension and is of independent interest. As a corollary of this entropy estimate, we obtain some quantitative bounds on the speed of convergence of the aforementioned hydrodynamic limit.

arXiv comment66 pages

References in corpus (4)

• Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions
• A stochastic Burgers equation from a class of microscopic interactions
• Weakly asymmetric bridges and the KPZ equation
• Non-equilibrium fluctuations for a reaction-diffusion model via relative entropy

Cited by in corpus (11)

• Sharp Convergence to Equilibrium for the SSEP with Reservoirs
• Higher order hydrodynamics and equilibrium fluctuations of interacting particle systems
• The stochastic heat equation as the limit of a stirring dynamics perturbed by a voter model
• Hyperbolic scaling limit of non-equilibrium fluctuations for a weakly anharmonic chain
• Non-equilibrium Fluctuations of the Weakly Asymmetric Normalized Binary Contact Path Process
• Spatial-segregation limit for exclusion processes with two components under unbalanced reaction
• Derivation of viscous Burgers equations from weakly asymmetric exclusion processes
• On the hydrodynamics of active matter models on a lattice
• The cutoff profile for exclusion processes in any dimension
• A one-phase Stefan problem with non-linear diffusion from highly competing two-species particle systems
• Hydrodynamic limit of the Kawasaki dynamics on the 1D-lattice with strong, finite-range interaction