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2015 Random walk driven by simple exclusion process
François Huveneers, François Simenhaus
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Electron. J. Probab. 20: 1-42 (2015). DOI: 10.1214/EJP.v20-3906


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.


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François Huveneers. François Simenhaus. "Random walk driven by simple exclusion process." Electron. J. Probab. 20 1 - 42, 2015.


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

zbMATH: 1328.60227
MathSciNet: MR3407222
Digital Object Identifier: 10.1214/EJP.v20-3906

Primary: 60K37
Secondary: 60F17


Vol.20 • 2015
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