Universal current fluctuations in the symmetric exclusion process and other diffusive systems

Using the macroscopic fluctuation theory of Bertini, De Sole, Gabrielli, Jona-Lasinio, and Landim, one can show that the statistics of the current of the symmetric simple exclusion process (SSEP) connected to two reservoirs on an arbitrary large finite domain in dimension d are the same as in the one-dimensional case. Numerical results on squares support this claim while results on cubes exhibit some discrepancy. We argue that the results of the macroscopic fluctuation theory should be recovered by increasing the size of the contacts. The generalization to other diffusive systems is straightforward.