Open Access
2023 Equilibrium perturbations for stochastic interacting systems
Lu Xu, Linjie Zhao
Author Affiliations +
Electron. J. Probab. 28: 1-30 (2023). DOI: 10.1214/22-EJP900


We consider the equilibrium perturbations for two stochastic systems: the d-dimensional generalized exclusion process and the one-dimensional chain of anharmonic oscillators. We add a perturbation of order Nα to the equilibrium profile and speed up the process by N1+κ for parameters 0<κα. Under some additional constraints on κ and α, we show the perturbed quantities evolve according to the Burgers equation in the exclusion process, and to two decoupled Burgers equations in the anharmonic chain, both in the smooth regime.

Funding Statement

Supported by the ANR grant MICMOV (ANR-19-CE40-0012) of the French National Research Agency (ANR) and the Fundamental Research Funds for the Central Universities in China.


Download Citation

Lu Xu. Linjie Zhao. "Equilibrium perturbations for stochastic interacting systems." Electron. J. Probab. 28 1 - 30, 2023.


Received: 5 June 2022; Accepted: 29 December 2022; Published: 2023
First available in Project Euclid: 5 January 2023

arXiv: 2206.01959
Digital Object Identifier: 10.1214/22-EJP900

Primary: 60K35 , 82C22

Keywords: equilibrium perturbation , Exclusion process , Hydrodynamic limit , oscillator chain

Vol.28 • 2023
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