Hydrodynamics for the partial exclusion process in random environment

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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).

Original languageEnglish
Pages (from-to)124-158
Number of pages35
JournalStochastic Processes and their Applications
Publication statusPublished - 2021


  • Arbitrary starting point quenched invariance principle
  • Duality
  • Hydrodynamic limit
  • Mild solution
  • Random conductance model
  • Random environment


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