Flux fluctuations in the one dimensional nearest neighbors symmetric simple exclusion process

Details Flux fluctuations in the one dimensional nearest neighbors symmetric simple exclusion process Flux fluctuations in the one dimensional nearest neighbors symmetric simple exclusion process

2001-03-30

arxiv.org/abs/math/0103233v2

J. Statist. Phys. 107 (2002), no. 3-4, 677--683

Mathematics

Probability

7 pages. A short discussion about the relationship of the flux fluctuations and the equilibrium density fluctuation fields was

Scientific paper

10.1023/A:1014577928229

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: \[ \lim_{t\to\infty} t^{-1/2} \V J(t) = \sqrt{2/\pi} (1-\rho)\rho \] 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, results previously proven by Arratia.

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