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