Transience of second-class particles and diffusive bounds for additive functionals in one-dimensional asymmetric and exclusion processes

Abstract

Consider a one-dimensional exclusion process with finite-range translation-invariant jump rates with nonzero drift. Let the process be stationary with product Bernoulli invariant distribution at density $\rho$. Place a second-class particle initially at the origin. For the case $\rho\neq 1/2$ we show that the time spent by the second-class particle at the origin has finite expectation. This strong transience is then used to prove that variances of additive functionals of local mean-zero functions are diffusive when $\rho\neq 1/2$. As a corollary to previous work, we deduce the invariance principle for these functionals. The main arguments are comparisons of $H_{-1}$ norms, a large deviation estimate for second-class particles and a relation between occupation times of second-class particles, and additive functional variances.