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2023 A note on the antisymmetry in the speed of a random walk in reversible dynamic random environment
Oriane Blondel
Author Affiliations +
Electron. Commun. Probab. 28: 1-6 (2023). DOI: 10.1214/23-ECP514

Abstract

In this short note, we prove that v(ε)=v(ε). Here, v(ε) 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 12+ε (resp. 12ε) if it stands on an occupied site, and vice-versa on an empty site. We work in any setting where v(ε),v(ε) 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

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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

Information

Received: 27 October 2022; Accepted: 20 January 2023; Published: 2023
First available in Project Euclid: 26 January 2023

MathSciNet: MR4543972
zbMATH: 1509.82058
Digital Object Identifier: 10.1214/23-ECP514

Subjects:
Primary: 60G50 , 82B41

Keywords: coupling , random walks in dynamic random environment , reversibility

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