Abstract
We introduce a family of stationary coupled Sasamoto-Spohn models and show that, in the weakly asymmetric regime, they converge to the energy solution of coupled Burgers equations. Moreover, we show that any system of coupled Burgers equations satisfying the so-called trilinear condition ensuring stationarity can be obtained as the scaling limit of a suitable system of coupled Sasamoto-Spohn models.
The core of our proof, which avoids the use of spectral gap estimates, consists in a second order Boltzmann-Gibbs principle for the discrete model.
Funding Statement
Partially supported by Fondecyt grants 1171257 and 1211189.
Acknowledgments
We are grateful to the anonymous referees and to Patricia Gonçalves and Santiago Saglietti for their valuable comments.
Citation
Ian Butelmann. Gregorio R. Moreno Flores. "Scaling limit of stationary coupled Sasamoto-Spohn models." Electron. J. Probab. 27 1 - 25, 2022. https://doi.org/10.1214/22-EJP819
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