Hydrodynamics for the partial exclusion process in random environment

Abstract

In this paper, we introduce a random environment for the exclusion process in ${\mathbb{Z}}^d$ obtained by assigning a maximal occupancy to each site. This maximal occupancy is allowed to randomly vary among sites, and partial exclusion occurs. Under the assumption of ergodicity under translation and uniform ellipticity of the environment, we derive a quenched hydrodynamic limit in path space by strengthening the mild solution approach initiated in [39] and [21]. To this purpose, we prove, employing the technology developed for the random conductance model, a homogenization result in the form of an arbitrary starting point quenched invariance principle for a single particle in the same environment, which is a result of independent interest. The self-duality property of the partial exclusion process allows us to transfer this homogenization result to the particle system and, then, apply the tightness criterion in [40].

34 pages, 1 figure

References in corpus (5)

• Duality and hidden symmetries in interacting particle systems
• Invariance principle for the random conductance model with unbounded conductances
• Scaling limits for gradient systems in random environment
• Hydrodynamic limit of symmetric exclusion processes in inhomogeneous media
• Stochastic homogenization in amorphous media and applications to exclusion processes

Cited by in corpus (6)

• Switching interacting particle systems: scaling limits, uphill diffusion and boundary layer
• Large Deviations in the Symmetric Simple Exclusion Process with Slow Boundaries: A Hydrodynamic Perspective
• Orthogonal polynomial duality of boundary driven particle systems and non-equilibrium correlations
• Hydrodynamical behavior for the generalized symmetric exclusion with open boundary
• From quenched invariance principle to semigroup convergence with applications to exclusion processes
• Mixing time for the asymmetric simple exclusion process in a random environment