Abstract
We simplify the proof of Spitzer’s recurrence criterion for homogeneous random walks on the integers. Kemperman’s oscillating random walk is next revisited and preliminaries for a Spitzer’s type result are established.
Acknowledgments
We thank the Editor for helping to end the reviewing process and the reviewer for useful remarks.
Citation
Julien Brémont. "On homogeneous and oscillating random walks on the integers." Probab. Surveys 20 87 - 112, 2023. https://doi.org/10.1214/23-PS13
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