Electronic Journal of Probability

Random walk driven by simple exclusion process

François Huveneers and François Simenhaus

Full-text: Open access

Abstract

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.

Article information

Source
Electron. J. Probab., Volume 20 (2015), paper no. 105, 42 pp.

Dates
Accepted: 9 October 2015
First available in Project Euclid: 4 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1465067211

Digital Object Identifier
doi:10.1214/EJP.v20-3906

Mathematical Reviews number (MathSciNet)
MR3407222

Zentralblatt MATH identifier
1328.60227

Subjects
Primary: 60K37: Processes in random environments
Secondary: 60F17: Functional limit theorems; invariance principles

Keywords
Random walk in dynamic random environment limit theorem renormalization renewal times

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

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


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