### 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 language | English (US) |
---|---|

Pages (from-to) | 148-169 |

Number of pages | 22 |

Journal | Annals of Probability |

Volume | 31 |

Issue number | 1 |

DOIs | |

State | Published - Jan 2003 |

Externally published | Yes |

### Fingerprint

### 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.

Research output: Contribution to journal › Article

*Annals of Probability*, vol. 31, no. 1, pp. 148-169. https://doi.org/10.1214/aop/1046294307

}

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 -