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

Abstract

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: \[ \lim_{t\to\infty} t^{-1/2} \V J(t) = \sqrt{2/π} (1-ρ)ρ\] 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.

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

References in corpus (1)

• A dynamic one-dimensional interface interacting with a wall

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