Central limit theorems for additive functionals of the simple exclusion process

Research output: Contribution to journalArticle

26 Scopus citations

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 languageEnglish (US)
Pages (from-to)277-302
Number of pages26
JournalAnnals of Probability
Volume28
Issue number1
DOIs
StatePublished - Jan 2000
Externally publishedYes

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

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