Order of current variance and diffusivity in the rate one totally asymmetric zero range process

Details Order of current variance and diffusivity in the rate one totally asymmetric zero range process Order of current variance and diffusivity in the rate one totally asymmetric zero range process

2008-04-09

arxiv.org/abs/0804.1397v2

Journal of Stat. Phys., 133:(1) pp. 59-78. (2008)

Mathematics

Probability

23 pages; some minor typos corrected

Scientific paper

10.1007/s10955-008-9604-1

We prove that the variance of the current across a characteristic is of order t^{2/3} in a stationary constant rate totally asymmetric zero range process, and that the diffusivity has order t^{1/3}. This is a step towards proving universality of this scaling behavior in the class of one-dimensional interacting systems with one conserved quantity and concave hydrodynamic flux. The proof proceeds via couplings to show the corresponding moment bounds for a second class particle. We build on the methods developed by Balazs-Seppalainen for asymmetric simple exclusion. However, some modifications were needed to handle the larger state space. Our results translate into t^{2/3}-order of variance of the tagged particle on the characteristics of totally asymmetric simple exclusion.

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