Some invariance principles for additive functionals of simple
exclusion with finite-range translation-invariant jump rates $p(i, j) = p(j
- i)$ in dimensions $d \geq1$ are established. A previous investigation
concentrated on the case of $p$ symmetric. The principal tools to take
care of nonreversibility, when $p$ is asymmetric, are invariance
principles for associated random variables and a “local
balance”estimate on the asymmetric generator of the process.
¶ As a by-product,we provide upper and lower bounds on some transition
probabilities for mean-zero asymmetric second-class particles,which are not
Markovian, that show they behave like their symmetric Markovian
counterparts.Also some estimates with respect to second-class particles with
drift are discussed.
¶ In addition,a dichotomy between the occupation time process limits
in $d =1$ and $d \geq 2$ for symmetric exclusion is shown. In the former,
the limit is fractional Brownian motion with parameter 3/4, and in the latter,
the usual Brownian motion.