Transience of second-class particles and diffusive bounds for additive functionals in one-dimensional asymmetric exclusion processes (Q1872327)

A second-class particle is placed initially at zero site in a one-dimensional exclusion process with finite range translation-invariant jump rates with nonzero drift. The process will be stationary with product Bernoulli invariant distribution with marginal \(\rho\). The authors show that for \(\rho\neq\frac{1}{2}\) the time spent by the second-class particle at the origin has finite expectation and then that variances of additive functionals of local mean-zero functions are diffusive. An invariance principle for these functionals is deduced. Comparisons of \(H_{-1}\), large deviations estimates and relations between occupation times and additive functional variances are considered.