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2024 Nonequilibrium moderate deviations from hydrodynamics of the simple symmetric exclusion process
Xiaofeng Xue
Author Affiliations +
Electron. Commun. Probab. 29: 1-16 (2024). DOI: 10.1214/24-ECP573


In this paper, we give the moderate deviation principle from the hydrodynamic limit of the simple symmetric exclusion process on the 1-dimensional torus starting from a nonequilibrium state, which extends the result given in Gao and Quastel (2003) about the case where the process starts from an equilibrium state. The exponential tightness of the scaled density field of the process and a replacement lemma play key roles in the proof of the main result. We utilize Grownwall’s inequality and the upper bound of the large deviation principle given in Kipnis, Olla and Varadhan (1989) to prove the above exponential tightness and the replacement lemma respectively in the absence of the invariance of the initial distribution.

Funding Statement

Supported by National Natural Science Foundation of China with grant number 12371142 and Fundamental Research Funds for the Central Universities with grant number 2022JBMC039.


We warmly thank the Referees and Associate Editor for their careful reading of the paper as well as their comments and suggestions.


Download Citation

Xiaofeng Xue. "Nonequilibrium moderate deviations from hydrodynamics of the simple symmetric exclusion process." Electron. Commun. Probab. 29 1 - 16, 2024.


Received: 15 May 2023; Accepted: 8 January 2024; Published: 2024
First available in Project Euclid: 23 February 2024

Digital Object Identifier: 10.1214/24-ECP573

Primary: 60F10 , 60K35

Keywords: Exponential tightness , Moderate deviation , Nonequilibrium , replacement lemma , simple symmetric exclusion process

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