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

Abstract : We show, using the macroscopic fluctuation theory of Bertini, De Sole, Gabrielli, Jona-Lasinio, and Landim, that the statistics of the current of the symmetric simple exclusion process (SSEP) connected to two reservoirs are the same on an arbitrary large finite domain in dimension $d$ 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.
Document type :
Journal articles
Domain :

https://hal.archives-ouvertes.fr/hal-01721369
Contributor : Thierry Bodineau <>
Submitted on : Friday, March 2, 2018 - 9:12:28 AM
Last modification on : Wednesday, August 12, 2020 - 10:45:35 AM

### Identifiers

• HAL Id : hal-01721369, version 1
• ARXIV : 1306.3145

### Citation

Eric Akkermans, Thierry Bodineau, Bernard Derrida, Ohad Shpielberg. Universal current fluctuations in the symmetric exclusion process and other diffusive systems. EPL - Europhysics Letters, European Physical Society/EDP Sciences/Società Italiana di Fisica/IOP Publishing, 2013, 103 (2). ⟨hal-01721369⟩

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