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

¹ Department of Physics, Technion, Israel Institute of Technology - 32000 Haifa, Israel
² Département de Mathématiques et Applications, Ecole Normale Supérieure - 45 rue dUlm, 75230 Paris cedex 05, France, EU
³ Laboratoire de Physique Statistique, Ecole Normale Supérieure, UPMC Paris 6, Université Paris Diderot, CNRS 24 rue Lhomond, 75231 Paris cedex 05, France, EU

Received: 13 June 2013
Accepted: 8 July 2013

Abstract

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.