Abstract
We study the asymptotic behaviour of the number of times the elephant random walk in the critical regime visits the origin. Our result entails that most zeros of the critical elephant random walk occur shortly before its last passage time at zero. Additionally, we derive the tail estimate of the first return time of the random walk.
Acknowledgments
I would like to express my gratitude to my supervisor Jean Bertoin for his patience and all the valuable discussions I had with him during the time I wrote this article. Also, I would like to thank the anonymous referees for valuable comments that improved the quality of the paper.
Citation
Zheng Fang. "How often does a critical elephant random walk return to origin." Electron. Commun. Probab. 29 1 - 12, 2024. https://doi.org/10.1214/24-ECP636
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