### Abstract

Resolvent H_{-1} norms with respect to simple exclusion processes play an important role in many problems with respect to additive functionals, tagged particles, and hydrodynamics, among other concerns. Here, general translation-invariant finite-range simple exclusion processes with and without a distinguished particle are considered. For the standard system of indistinguishable particles, it is proved that the corresponding H_{-1} norms are equivalent, in a sense, to the H_{-1} norms of a nearest-neighbor system. The same result holds for systems with a distinguished particle in dimensions d ≥ 2. However, in dimension d = 1, this equivalence does not hold. An application of the H_{-1} norm equivalence to additive functional variances is also given.

Original language | English (US) |
---|---|

Pages (from-to) | 35-62 |

Number of pages | 28 |

Journal | Annals of Probability |

Volume | 31 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2003 |

Externally published | Yes |

### Fingerprint

### Keywords

- Simple exclusion process H
- Variance norms

### ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty