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) |
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Pages (from-to) | 35-62 |
Number of pages | 28 |
Journal | Annals of Probability |
Volume | 31 |
Issue number | 1 |
DOIs | |
State | Published - Jan 2003 |
Externally published | Yes |
Keywords
- Simple exclusion process H
- Variance norms
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty