Central limit theorems for additive functionals of the simple exclusion process

Research output: Contribution to journalArticle

26 Citations (Scopus)

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
StatePublished - Jan 2000
Externally publishedYes

Fingerprint

Additive Functionals
Exclusion Process
Second Class Particle
Central limit theorem
Invariance Principle
Associated Random Variables
Occupation Time
Fractional Brownian Motion
Dichotomy
Transition Probability
Estimate
Brownian motion
Upper and Lower Bounds
Jump
Generator
Invariant
Zero
Range of data
Exclusion
Invariance

Keywords

  • Associated
  • Central limit theorem
  • FKG
  • Invariance principle
  • Second-class particles
  • Simple exclusion process

ASJC Scopus subject areas

  • Mathematics(all)
  • Statistics and Probability

Cite this

Central limit theorems for additive functionals of the simple exclusion process. / Sethuraman, Sunder.

In: Annals of Probability, Vol. 28, No. 1, 01.2000, p. 277-302.

Research output: Contribution to journalArticle

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