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Equilibrium Fluctuations for the Totally Asymmetric Zero-Range Process

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Abstract

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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  1. Centro de Matemática da Universidade do Minho, Campus de Gualtar, 4710-057, Braga, Portugal

    Patrícia Gonçalves

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  1. Patrícia Gonçalves
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Correspondence to Patrícia Gonçalves.

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Gonçalves, P. Equilibrium Fluctuations for the Totally Asymmetric Zero-Range Process. J Stat Phys 138, 645–661 (2010). https://doi.org/10.1007/s10955-009-9888-9

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  • DOI: https://doi.org/10.1007/s10955-009-9888-9

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