Random walk driven by the simple exclusion process

Abstract

We prove a 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 of the walker, 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 the fluctuations are normal.

v2 -> v3: Figures and heuristic comments added. Various typos corrected

References in corpus (5)

• Geometry-induced superdiffusion in driven crowded systems
• Random walk in Markovian environment
• The Point of View of the Particle on the Law of Large Numbers for Random Walks in a Mixing Random Environment
• Mobility transition in a dynamic environment
• Random walks in space time mixing environments

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• A Driven Tagged Particle in Symmetric Exclusion Processes with Removals
• Limiting distributions for RWCRE in the sub-ballistic regime and in the critical Gaussian regime
• Absolute Continuity and Weak Uniform Mixing of Random Walk in Dynamic Random Environment
• Law of large numbers for ballistic random walks in dynamic random environments under lateral decoupling