Law of Large Numbers for a Class of Random Walks in Dynamic Random Environments
TLDR
In this article, a class of one-dimensional interacting particle systems in equilibrium, constituting a dynamic random environment, together with a nearest-neighbor random walk that on occupied/vacant sites has a local drift to the right/left.Abstract:
In this paper we consider a class of one-dimensional interacting particle systems in equilibrium, constituting a dynamic random environment, together with a nearest-neighbor random walk that on occupied/vacant sites has a local drift to the right/left. We adapt a regeneration-time argument originally developed by Comets and Zeitouni for static random environments to prove that, under a space-time mixing property for the dynamic random environment called cone-mixing, the random walk has an a.s. constant global speed. In addition, we show that if the dynamic random environment is exponentially mixing in space-time and the local drifts are small, then the global speed can be written as a power series in the size of the local drifts. From the first term in this series the sign of the global speed can be read off. The results can be easily extended to higher dimensions.read more
Citations
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Random walk on random walks
Marcelo R. Hilario,Frank den Hollander,Vladas Sidoravicius,Renato Soares dos Santos,Augusto Teixeira +4 more
TL;DR: In this article, the authors studied a random walk in a one-dimensional dynamic random environment and showed 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 the deviation bound is large enough.
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Random walks in dynamic random environments: A transference principle
Frank Redig,Florian Völlering +1 more
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Random walks in dynamic random environments: A transference principle
Frank Redig,Florian Völlering +1 more
TL;DR: In this paper, a general class of random walks driven by a uniquely ergodic Markovian environment is studied and the authors obtain strong ergodicity properties for the environment as seen from the position of the walker, that is, the environment process.
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Scaling of a random walk on a supercritical contact process
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TL;DR: You have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use.
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