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We prove that the variance of the current across a characteristic is of ordert^{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 provinguniversality of this scaling behavior in the class of one-dimensionalinteracting systems with one conserved quantity and concave hydrodynamic flux.The proof proceeds via couplings to show the corresponding moment bounds for asecond class particle. We build on the methods developed by Balazs-Seppalainenfor asymmetric simple exclusion. However, some modifications were needed tohandle the larger state space. Our results translate into t^{2/3}-order ofvariance of the tagged particle on the characteristics of totally asymmetricsimple exclusion.

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