Fluctuations in the occupation time of a site in the asymmetric simple exclusion process

Abstract

We consider the simple asymmetric exclusion process with nonzero drift under the stationary Bernoulli product measure at density $\rho$. We prove that for dimension $d=2$ the occupation time of the site 0 is diffusive as soon as $\rho\neq 1/2$. For dimension $d=1$, if the density $\rho$ is equal to $1/2$, we prove that the time t variance of the occupation time of the site 0 diverges in a certain sense at least as $t^{5/4}$.