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2023 Simple random walk on Z2 perturbed on the axes (renewal case)
Pierre Andreoletti, Pierre Debs
Author Affiliations +
Electron. J. Probab. 28: 1-25 (2023). DOI: 10.1214/23-EJP969

Abstract

We study a simple random walk on Z2 with constraints on the axes. Motivation comes from physics when particles (a gas for example) are submitted to a local field. In our case we assume that a particle evolves freely in the cones but when touching the axes a force pushes it back progressively to the origin. The main result proves that this force can be parametrized in such a way that a renewal structure appears in the trajectory of the random walk. This implies the existence of an ergodic result for the parts of the trajectory restricted to the axes.

Acknowledgments

We would like to thank Julien Barré for introducing us the work of physicists and the problematics which inspire this paper.

Citation

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Pierre Andreoletti. Pierre Debs. "Simple random walk on Z2 perturbed on the axes (renewal case)." Electron. J. Probab. 28 1 - 25, 2023. https://doi.org/10.1214/23-EJP969

Information

Received: 2 December 2022; Accepted: 7 June 2023; Published: 2023
First available in Project Euclid: 5 September 2023

MathSciNet: MR4636772
Digital Object Identifier: 10.1214/23-EJP969

Subjects:
Primary: 05C81 , 60J10 , 60J55 , 60K10 , 60K40

Keywords: ergodic theorem , perturbed random walks , Renewal theorem

Vol.28 • 2023
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