### Abstract

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 ≥ 1 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 ≥ 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.

Original language | English (US) |
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Pages (from-to) | 277-302 |

Number of pages | 26 |

Journal | Annals of Probability |

Volume | 28 |

Issue number | 1 |

DOIs | |

State | Published - Jan 2000 |

Externally published | Yes |

### Keywords

- Associated
- Central limit theorem
- FKG
- Invariance principle
- Second-class particles
- Simple exclusion process

### ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty