### 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 ρ. Place a second-class particle initially at the origin. For the case ≠ 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 ≠ 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.

Original language | English (US) |
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Pages (from-to) | 148-169 |

Number of pages | 22 |

Journal | Annals of Probability |

Volume | 31 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2003 |

Externally published | Yes |

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### Keywords

- Additive functionals
- Exclusion process
- Invariance principle
- Second-class particle

### ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty