Transience of second-class particles and diffusive bounds for additive functionals in one-dimensional asymmetric exclusion processes

Timo Seppäläinen, Sunder Sethuraman

Research output: Contribution to journalArticle

6 Scopus citations

Abstract

Consider a one-dimensional exclusion process with finite-range translation-invariant jump rates with nonzero drift. Let the process be stationary with product Bernoulli invariant distribution at density ρ. Place a second-class particle initially at the origin. For the case ≠ 1/2 we show that the time spent by the second-class particle at the origin has finite expectation. This strong transience is then used to prove that variances of additive functionals of local mean-zero functions are diffusive when ≠ 1/2. As a corollary to previous work, we deduce the invariance principle for these functionals. The main arguments are comparisons of H-1 norms, a large deviation estimate for second-class particles and a relation between occupation times of second-class particles, and additive functional variances.

Original languageEnglish (US)
Pages (from-to)148-169
Number of pages22
JournalAnnals of Probability
Volume31
Issue number1
DOIs
StatePublished - Jan 1 2003
Externally publishedYes

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Keywords

  • Additive functionals
  • Exclusion process
  • Invariance principle
  • Second-class particle

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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