Hydrodynamics for the partial exclusion process in random environment

Floreani, S.; Redig, F.H.J.; Sau, Federico

doi:10.1016/j.spa.2021.08.006

Hydrodynamics for the partial exclusion process in random environment

Title

Hydrodynamics for the partial exclusion process in random environment

Author

Floreani, S. (TU Delft Applied Probability)
Redig, F.H.J. (TU Delft Applied Probability)
Sau, Federico (Institute of Science and Technology (IST Austria))

Date

2021

Abstract

In this paper, we introduce a random environment for the exclusion process in 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 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).

Subject

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

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http://resolver.tudelft.nl/uuid:8c8432c0-8e2e-4de3-aa6d-6c27210d36ea

DOI

https://doi.org/10.1016/j.spa.2021.08.006

ISSN

0304-4149

Source

Stochastic Processes and their Applications, 142, 124-158

Part of collection

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