Abstract
AbstractConsider a generalized model of the facilitated exclusion process, which is a one-dimensional exclusion process with a dynamical constraint that prevents the particle at site x from jumping to x + 1 (or x − 1) if the sites x − 1, x − 2 (or x + 1, x + 2) are empty. It is non-gradient and lacks invariant measures of product form. The purpose of this paper is to identify the invariant measures and to show that they satisfy both exponential decay of correlations and equivalence of ensembles. These properties will play a pivotal role in deriving the hydrodynamic limit.
Publisher
Springer Science and Business Media LLC
Reference9 articles.
1. O Blondel, C Erignoux, M Sasada, M Simon. Hydrodynamic limit for a facilitated exclusion process, Ann Inst Henri Poincaré Probab Stat, 2020, 56(1): 667–714.
2. P Gonçalves, C Landim, C Toninelli. Hydrodynamic limit for a particle system with degenerate rates, Ann Inst Henri Poincaré Probab Stat, 2009, 45(4): 887–909.
3. C Kipnis, C Landim. Scaling limits of interacting particle systems, Grundlehren der Mathematischen Wissenschaften, Springer-Verlag, Berlin, 1999, 320.
4. Y Lei, Z Su. Hydrodynamic limit for the d-facilitated exclusion process (preprint).
5. T Liggett. Interacting particle systems. Classics in Mathematics, Springer-Verlag, Berlin, 2005.