Abstract
In this paper we study a random walk in a one-dimensional dynamic random environment consisting of a collection of independent particles performing simple symmetric random walks in a Poisson equilibrium with density $\rho \in (0,\infty)$. At each step the random walk performs a nearest-neighbour jump, moving to the right with probability $p_{\circ}$ when it is on a vacant site and probability $p_{\bullet}$ when it is on an occupied site. Assuming that $p_\circ \in (0,1)$ and $p_\bullet \neq \tfrac12$, we show that the position of the random walk satisfies a strong law of large numbers, a functional central limit theorem and a large deviation bound, provided $\rho$ is large enough. The proof is based on the construction of a renewal structure together with a multiscale renormalisation argument.
Citation
Marcelo Hilário. Frank den Hollander. Vladas Sidoravicius. Renato Soares dos Santos. Augusto Teixeira. "Random walk on random walks." Electron. J. Probab. 20 1 - 35, 2015. https://doi.org/10.1214/EJP.v20-4437
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