Strong Asymmetric Limit of the Quasi-Potential of the Boundary Driven Weakly Asymmetric Exclusion Process

2008/06/13 by Lorenzo Bertini, Davide Gabrielli, Claudio Landim +1 · 17 citations
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Asymmetric simple exclusion process #Asymmetry #Boundary (topology) #Boundary value problem #Bounded function #Combinatorics #Dirichlet boundary condition #Geometry #Interval (graph theory) #Limit (mathematics) #Markov Chains and Monte Carlo Methods #Mathematical analysis #Mathematics #Physics #Quantum mechanics #Scaling #Scaling limit #Statistical physics #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #Thermodynamic limit #math-ph #math.MP #math.PR #msc:60F10 #msc:82C22 #msc:82C35

paper · pdf · doi:10.1007/s00220-009-0751-2

published in Communications in Mathematical Physics 289(1), 311-334 (Springer Science+Business Media)

arxiv created 2008/06/13 · openalex publication_date 2009/02/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

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 equation with Dirichlet boundary conditions. In the case in which the bulk asymmetry is in the same direction as the drift due to the boundary reservoirs, we prove that the quasi-potential can be expressed in terms of the solution to a one-dimensional boundary value problem which has been introduced by Enaud and Derrida \citede. We consider the strong asymmetric limit of the quasi-potential and recover the functional derived by Derrida, Lebowitz, and Speer \citeDLS3 for the asymmetric exclusion process.

Citations

• Static large deviations of boundary driven exclusion processes
• Current Large Deviations for Asymmetric Exclusion Processes with Open Boundaries
• Macroscopic Fluctuation Theory for Stationary Non-Equilibrium States

Cited by

• Large deviation principles for nongradient weakly asymmetric stochastic lattice gases
• Current Fluctuations in One Dimensional Diffusive Systems with a Step Initial Density Profile

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