Using the recently discovered strong negative dependence properties of the symmetric exclusion process, we derive general conditions for when the normalized current of particles between regions converges to the Gaussian distribution. The main novelty is that the results do not assume any translation invariance, and hold for most initial configurations.
Alexander Vandenberg-Rodes. "A limit theorem for particle current in the symmetric exclusion process." Electron. Commun. Probab. 15 240 - 252, 2010. https://doi.org/10.1214/ECP.v15-1550