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Flux fluctuations in the one dimensional nearest neighbors symmetric simple exclusion process. (English) Zbl 1008.82022
Summary: Let \(J(t)\) be the the integrated flux of particles in the symmetric simple exclusion process starting with the product invariant measure \(\nu_\rho\) with density \(\rho\). We compute its rescaled asymptotic variance: \[ \lim_{t \rightarrow \infty} t^{-1/2} {\mathbb V} J(t)=\sqrt{2/ \pi} (1-\rho) \rho \] Furthermore we show that \(t^{-1/4}J(t)\) converges weakly to a centered normal random variable with this variance. From these results we compute the asymptotic variance of a tagged particle in the nearest neighbor case and show the corresponding central limit theorem.

MSC:
82C22 Interacting particle systems in time-dependent statistical mechanics
60K35 Interacting random processes; statistical mechanics type models; percolation theory
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