Abstract
In this short note, we prove that . Here, is the speed of a one-dimensional random walk in a dynamic reversible random environment, that jumps to the right (resp. to the left) with probability (resp. ) if it stands on an occupied site, and vice-versa on an empty site. We work in any setting where are well-defined, i.e. a weak LLN holds. The proof relies on a simple coupling argument that holds only in the discrete setting.
Citation
Oriane Blondel. "A note on the antisymmetry in the speed of a random walk in reversible dynamic random environment." Electron. Commun. Probab. 28 1 - 6, 2023. https://doi.org/10.1214/23-ECP514
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