How often does a critical elephant random walk return to origin
Probability
2024-10-10 v2
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.
Cite
@article{arxiv.2406.02399,
title = {How often does a critical elephant random walk return to origin},
author = {Zheng Fang},
journal= {arXiv preprint arXiv:2406.02399},
year = {2024}
}
Comments
13 pages, 1 figure; this version contains a few minor modifications to improve the readability. Comments are welcome!