Abstract
We provide a full description for the joint fluctuations of current and occupation time in the one-dimensional nonequilibrium simple symmetric exclusion process, furnishing explicit formulas for the covariances of the limiting Gaussian process. The main novelties consist of a proof of the tightness of the nonequilibrium current based on new correlation estimates, refined estimates on the discrete gradient of the transition probabilities of the SSEP, and a nonequilibrium Kipnis-Varadhan Lemma based on a Fourier approach.
Acknowledgments
D.E. was supported by the National Council for Scientific and Technological Development – CNPq via a Bolsa de Produtividade 303520/2019-1 and 303348/2022-4. D.E. and T.Xu moreover acknowledge support by the Serrapilheira Institute (Grant Number Serra-R-2011-37582). D.E and T.F. moreover acknowledge support by the National Council for Scientific and Technological Development – CNPq via a Universal Grant (Grant Number 406001/2021-9). T.F was supported by the National Council for Scientific and Technological Development – CNPq via a Bolsa de Produtividade number 311894/2021-6.
Citation
Dirk Erhard. Tertuliano Franco. Tiecheng Xu. "Nonequilibrium joint fluctuations for current and occupation time in the symmetric exclusion process." Electron. J. Probab. 29 1 - 53, 2024. https://doi.org/10.1214/24-EJP1137
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