CURRENT FLUCTUATIONS FOR THE ASYMMETRIC SIMPLE EXCLUSION PROCESS

We compute the diffusion coefficient of the current of particles throu gh a fixed point in the one-dimensional nearest neighbor asymmetric si mple exclusion process in equilibrium. We find D = \p - q\rho(1 - rho) \1 - 2rho\, where p is the rate at which the particles jump to the rig ht, q is the jump rate to the left and rho is the density of particles . Notice that D vanishes if p = q or rho = 1/2. Laws of large numbers and central limit theorems are also proven. Analogous results are obta ined for the current of particles through a position travelling at a d eterministic velocity r. As a corollary we get that the equilibrium de nsity fluctuations at time t are a translation of the fluctuations at time 0. We also show that the current fluctuations at time t are given , in the scale t1/2, by the initial density of particles in an interva l of length \(p - q)(1 - 2rho)\t. The process is isomorphic to a growt h interface process. Our result means that the equilibrium growth fluc tuations depend on the general inclination of the surface. In particul ar, they vanish for interfaces roughly perpendicular to the observed g rowth direction.