Mathematics – Probability
Scientific paper
2001-08-24
Ann. Probab. 31 (2003), 148-169
Mathematics
Probability
22 pages
Scientific paper
Consider a one-dimensional exclusion process with finite-range translation-invariant jump rates with non-zero 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 different from 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 is not 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.
Seppalainen Timo
Sethuraman Sunder
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