An equivalence of H-1 norms for the simple exclusion process

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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 languageEnglish (US)
Pages (from-to)35-62
Number of pages28
JournalAnnals of Probability
Volume31
Issue number1
DOIs
StatePublished - Jan 1 2003
Externally publishedYes

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Keywords

  • Simple exclusion process H
  • Variance norms

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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