Electronic Journal of Probability
- Electron. J. Probab.
- Volume 20 (2015), paper no. 105, 42 pp.
Random walk driven by simple exclusion process
We prove strong law of large numbers and an annealed invariance principle for a random walk in a one-dimensional dynamic random environment evolving as the simple exclusion process with jump parameter $\gamma$. First we establish that, if the asymptotic velocity of the walker is non-zero in the limiting case "$\gamma = \infty$" where the environment gets fully refreshed between each step, then, for $\gamma$ large enough, the walker still has a non-zero asymptotic velocity in the same direction. Second we establish that if the walker is transient in the limiting case $\gamma = 0$, then, for $\gamma$ small enough but positive, the walker has a non-zero asymptotic velocity in the direction of the transience. These two limiting velocities can sometimes be of opposite sign. In all cases, we show that fluctuations are normal.
Electron. J. Probab., Volume 20 (2015), paper no. 105, 42 pp.
Accepted: 9 October 2015
First available in Project Euclid: 4 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60K37: Processes in random environments
Secondary: 60F17: Functional limit theorems; invariance principles
This work is licensed under aCreative Commons Attribution 3.0 License.
Huveneers, François; Simenhaus, François. Random walk driven by simple exclusion process. Electron. J. Probab. 20 (2015), paper no. 105, 42 pp. doi:10.1214/EJP.v20-3906. https://projecteuclid.org/euclid.ejp/1465067211