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 Citations (Scopus)

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 2003
Externally publishedYes

Fingerprint

Second Class Particle
Additive Functionals
Asymmetric Exclusion Process
Transience
Additive Functional
Occupation Time
Exclusion Process
Invariant Distribution
Invariance Principle
Large Deviations
Bernoulli
Deduce
Corollary
Jump
Norm
Invariant
Exclusion
Zero
Estimate
Range of data

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Statistics and Probability

Cite this

Transience of second-class particles and diffusive bounds for additive functionals in one-dimensional asymmetric exclusion processes. / Seppäläinen, Timo; Sethuraman, Sunder.

In: Annals of Probability, Vol. 31, No. 1, 01.2003, p. 148-169.

Research output: Contribution to journalArticle

@article{0ea21758339b44d4b68eee85abd2534a,
title = "Transience of second-class particles and diffusive bounds for additive functionals in one-dimensional asymmetric exclusion processes",
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.",
keywords = "Additive functionals, Exclusion process, Invariance principle, Second-class particle",
author = "Timo Sepp{\"a}l{\"a}inen and Sunder Sethuraman",
year = "2003",
month = "1",
doi = "10.1214/aop/1046294307",
language = "English (US)",
volume = "31",
pages = "148--169",
journal = "Annals of Probability",
issn = "0091-1798",
publisher = "Institute of Mathematical Statistics",
number = "1",

}

TY - JOUR

T1 - Transience of second-class particles and diffusive bounds for additive functionals in one-dimensional asymmetric exclusion processes

AU - Seppäläinen, Timo

AU - Sethuraman, Sunder

PY - 2003/1

Y1 - 2003/1

N2 - 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.

AB - 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.

KW - Additive functionals

KW - Exclusion process

KW - Invariance principle

KW - Second-class particle

UR - http://www.scopus.com/inward/record.url?scp=0037248539&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0037248539&partnerID=8YFLogxK

U2 - 10.1214/aop/1046294307

DO - 10.1214/aop/1046294307

M3 - Article

AN - SCOPUS:0037248539

VL - 31

SP - 148

EP - 169

JO - Annals of Probability

JF - Annals of Probability

SN - 0091-1798

IS - 1

ER -