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2015 Random walk on random walks
Marcelo Hilário, Frank den Hollander, Vladas Sidoravicius, Renato Soares dos Santos, Augusto Teixeira
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Electron. J. Probab. 20: 1-35 (2015). DOI: 10.1214/EJP.v20-4437

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.

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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

Information

Accepted: 12 September 2015; Published: 2015
First available in Project Euclid: 4 June 2016

zbMATH: 1328.60226
MathSciNet: MR3399831
Digital Object Identifier: 10.1214/EJP.v20-4437

Subjects:
Primary: 60F15, 60K35, 60K37
Secondary: 82B41, 82C22, 82C44

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