## The Annals of Probability

### Transience of second-class particles and diffusive bounds for additive functionals in one-dimensional asymmetric and 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 $\rho$. Place a second-class particle initially at the origin. For the case $\rho\neq 1/2$ 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 $\rho\neq 1/2$. 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.

#### Article information

Source
Ann. Probab., Volume 31, Number 1 (2003), 148-169.

Dates
First available in Project Euclid: 26 February 2003

https://projecteuclid.org/euclid.aop/1046294307

Digital Object Identifier
doi:10.1214/aop/1046294307

Mathematical Reviews number (MathSciNet)
MR1959789

Zentralblatt MATH identifier
1029.60083

#### Citation

Seppäläinen, Timo; Sethuraman, Sunder. Transience of second-class particles and diffusive bounds for additive functionals in one-dimensional asymmetric and exclusion processes. Ann. Probab. 31 (2003), no. 1, 148--169. doi:10.1214/aop/1046294307. https://projecteuclid.org/euclid.aop/1046294307

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• MADISON, WISCONSIN 53706-1388 E-MAIL: seppalai@math.wisc.edu DEPARTMENT OF MATHEMATICS IOWA STATE UNIVERSITY 400 CARVER HALL
• AMES, IOWA 50011 E-MAIL: sethuram@iastate.edu