Floreani, Simone; Redig, Frank; Sau, FedericoIST Austria
In this paper, we introduce a random environment for the exclusion process in 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).
Stochastic Processes and their Applications
The authors would like to thank Marek Biskup and Alberto Chiarini for useful suggestions and Cristian Giardina, Frank den Hollander and Shubhamoy Nandan for inspiring discussions. S.F. acknowledges Simona Villa for her help in creating the picture. Furthermore, the authors thank two anonymous referees for the careful reading of the manuscript. S.F. acknowledges financial support from NWO, The Netherlands via the grant TOP1.17.019. F.S. acknowledges financial support from NWO via the TOP1 grant 613.001.552 as well as funding from the European Union’s Horizon 2020 research and innovation programme under the Marie-Skłodowska-Curie grant agreement No. 754411.
Floreani S, Redig F, Sau F. Hydrodynamics for the partial exclusion process in random environment. Stochastic Processes and their Applications. 2021;142:124-158. doi:10.1016/j.spa.2021.08.006
Floreani, S., Redig, F., & Sau, F. (2021). Hydrodynamics for the partial exclusion process in random environment. Stochastic Processes and Their Applications. Elsevier. https://doi.org/10.1016/j.spa.2021.08.006
Floreani, Simone, Frank Redig, and Federico Sau. “Hydrodynamics for the Partial Exclusion Process in Random Environment.” Stochastic Processes and Their Applications. Elsevier, 2021. https://doi.org/10.1016/j.spa.2021.08.006.
S. Floreani, F. Redig, and F. Sau, “Hydrodynamics for the partial exclusion process in random environment,” Stochastic Processes and their Applications, vol. 142. Elsevier, pp. 124–158, 2021.
Floreani S, Redig F, Sau F. 2021. Hydrodynamics for the partial exclusion process in random environment. Stochastic Processes and their Applications. 142, 124–158.
Floreani, Simone, et al. “Hydrodynamics for the Partial Exclusion Process in Random Environment.” Stochastic Processes and Their Applications, vol. 142, Elsevier, 2021, pp. 124–58, doi:10.1016/j.spa.2021.08.006.
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