Hydrodynamics for the partial exclusion process in random environment

Simone Floreani, Frank Redig and Federico Sau

Stochastic Processes and their Applications, 2021, vol. 142, issue C, 124-158

Abstract: In this paper, we introduce a random environment for the exclusion process in Zd 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 Nagy (2002) and Faggionato (2007). 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 Redig et al. (2020).

Keywords: Hydrodynamic limit; Random environment; Random conductance model; Arbitrary starting point quenched invariance principle; Duality; Mild solution (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.spa.2021.08.006

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