Abstract
We derive the hydrodynamic limit for two degenerate lattice gases, the facilitated exclusion process (FEP) and the facilitated zero-range process (FZRP), both in the symmetric and the asymmetric case. For both processes, the hydrodynamic limit in the symmetric case takes the form of a diffusive Stefan problem, whereas the asymmetric case is characterized by a hyperbolic Stefan problem. Although the FZRP is attractive, a property that we extensively use to derive its hydrodynamic limits in both cases, the FEP is not. To derive the hydrodynamic limit for the latter, we exploit that of the zero-range process, together with a classical mapping between exclusion and zero-range processes, both at the microscopic and macroscopic level. Due to the degeneracy of both processes, the asymmetric case is a new result, but our work also provides a simpler proof than the one that was previously proposed for the FEP in the symmetric case in (Probab. Math. Phys. 2 (2021) 127–178).
Funding Statement
This project is partially supported by the ANR Grant MICMOV (ANR-19-CE40-0012) of the French National Research Agency (ANR), and by the European Union with the program FEDER “Fonds européen de développement régional” with the Région Hauts-de-France. It has also received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovative program (grant agreement n° 715734), from Labex CEMPI (ANR-11-LABX-0007-01), from the Fundamental Research Funds for the Central Universities and Hubei Key Laboratory of Engineering Modeling and Scientific Computing in China, and from the National Natural Science Foundation of China with grant numbers 11971038 and 12371142.
Acknowledgments
We warmly thank the anonymous referees for their careful reading and remarks which contributed to a better version of this paper. This work has been done while M. Simon was appointed at Gran Sasso Science Institute (GSSI), L’Aquila, Italy.
Data sharing not applicable to this article as no datasets were generated or analyzed during the current study.
Citation
Clément Erignoux. Marielle Simon. Linjie Zhao. "Mapping hydrodynamics for the facilitated exclusion and zero-range processes." Ann. Appl. Probab. 34 (1B) 1524 - 1570, February 2024. https://doi.org/10.1214/23-AAP1997
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