Equilibrium Fluctuations for the Totally Asymmetric Zero-Range Process
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We consider the one-dimensional Totally Asymmetric Zero-Range process evolving on ℤ and starting from the Geometric product measure ν ρ . On the hyperbolic time scale the temporal evolution of the limit density fluctuation field is deterministic, in the sense that the limit field at time t is a translation of the initial one. We consider the system in a reference frame moving at this velocity and we show that the limit density fluctuation field does not evolve in time until N 4/3, which implies the current across a characteristic to vanish on this longer time scale.
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