DYNAMICAL LARGE DEVIATIONS FOR THE BOUNDARY DRIVEN WEAKLY ASYMMETRIC EXCLUSION PROCESS

DYNAMICAL LARGE DEVIATIONS FOR THE BOUNDARY DRIVEN WEAKLY ASYMMETRIC EXCLUSION PROCESS

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 equation with Dirichlet boundary conditions. We prove the associat...

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Veröffentlicht in:The Annals of probability 2009-11, Vol.37 (6), p.2357-2403
Hauptverfasser: Bertini, Lorenzo, Landim, Claudio, Mourragui, Mustapha
Format: Artikel
Sprache:eng
Schlagworte:
60F10
82C22
82C35
Asymptotic methods
Boundary conditions
Cauchy Schwarz inequality
Density
Dot product of vectors
Exclusion
Exclusion process
Free energy
Hydrodynamic equations
Hydrodynamics
large deviations
Mathematical lattices
Particle interactions
Standard deviation
stationary nonequilibrium states
Stochastic models
Studies
Trajectories
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Beschreibung
Zusammenfassung: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 equation with Dirichlet boundary conditions. We prove the associated dynamical large deviations principle.
ISSN:0091-1798
2168-894X
DOI:10.1214/09-aop472