Current fluctuations in the zero-range process with open boundaries

Abstract

We discuss the long-time limit of the integrated current distribution for the one-dimensional zero-range process with open boundaries. We observe that the current fluctuations become site-dependent above some critical current and argue that this is a precursor of the condensation transition which occurs in such models. Our considerations for the totally asymmetric zero-range process are complemented by a Bethe ansatz treatment for the equivalent exclusion process.

25 pages, 6 figures. v2: refined argument in Sec. 3, removed appendix, fixed typos + updated references. v3: some changes in wording to make clear that we consider the case of fixed initial particle configuration. To be published in Journal of Statistical Mechanics: Theory and Experiment, IOP Publishing Ltd, http://www.iop.org