Flux fluctuations in the one dimensional nearest neighbors simple exclusion process

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-->infinity) t(-1/2)VJ(t) = root2/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. variance of a tagged particle in the nearest neighbor case and show the corresponding central limit theorem.