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.
@article{1046294307,
author = {Sepp\"al\"ainen, Timo and Sethuraman, Sunder},
title = {Transience of second-class particles and diffusive bounds for additive functionals in one-dimensional asymmetric and exclusion processes},
journal = {Ann. Probab.},
volume = {31},
number = {1},
year = {2003},
pages = { 148-169},
language = {en},
url = {http://dml.mathdoc.fr/item/1046294307}
}
Seppäläinen, Timo; Sethuraman, Sunder. Transience of second-class particles and diffusive bounds for additive functionals in one-dimensional asymmetric and exclusion processes. Ann. Probab., Tome 31 (2003) no. 1, pp. 148-169. http://gdmltest.u-ga.fr/item/1046294307/