How often does a critical elephant random walk return to origin

Zheng Fang

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arXiv · 2406.02399

How often does a critical elephant random walk return to origin

Zheng Fang

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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.

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Zheng Fang. 2024-06-04. How often does a critical elephant random walk return to origin. https://arxiv.org/abs/2406.02399

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