Equilibrium Fluctuations for the Totally Asymmetric Zero Range process

Details Equilibrium Fluctuations for the Totally Asymmetric Zero Range process Equilibrium Fluctuations for the Totally Asymmetric Zero Range process

2009-02-23

arxiv.org/abs/0902.3974v1

Mathematics

Probability

10 pages, no figures

Scientific paper

We prove a Central Limit Theorem for the empirical measure in the one-dimensional Totally Asymmetric Zero-Range Process in the hyperbolic scaling $N$, starting from the equilibrium measure $\nu_{\rho}$. We also show that when taking the direction of the characteristics, the limit density fluctuation field does not evolve in time until $N^{4/3}$, which implies the current across the characteristics to vanish in this longer time scale.

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